ACFI3309 FINANCIAL DERIVATIVES – TERM 2 WEEK 15: FX & INTEREST SWAPS 1. What is FX & Interest swap?  2. How to share risk and reduce costs using FX & Interest swap.  3. Be able to set FX & Interest swap strategy.   Previously considered: ◦ Same Currency, Fixed for Floating ◦ Same Currency, Floating for Floating • Conversely, currency swaps are a foreign exchange agreement between two parties to exchange cash flow streams in one currency to another. While currency swaps involve two currencies, interest rate swaps only deal with one currency.  Also: ◦ Different Currency, Fixed for Floating ◦ Different Currency, Floating for Floating SWAP VARIANTS Same currency, floating for floating  Company A can borrow floating at LIBOR + 1% or indexed to FTSE100 – 2.5%.  Company B can borrow floating at LIBOR + 1.75% or indexed to the FTSE100 -1%  Assuming A prefer LIBOR and B prefer FTSE100.  L F A L+1 Pref F-2.5 B L+1.75 F-1 Pref SAME CURRENCY FLOATING FOR FLOATING A UK company wants to expand into Japan, would like to borrow floating and is offered TIBOR + 1% (it can borrow locally at LIBOR + 0.4%).  A Japanese company wants to expand into the UK, would like to borrow floating and is offered LIBOR + 2% (it can borrow locally at TIBOR + 1.2%).  Assuming bank fee is 0.25%  L T UK L+0.4 T+1 Pref Japan L+2 Pref T+1.2 DIFFERENT CURRENCY, FLOATING FOR FLOATING Advantages Disadvantages Easy to arrange Legal and Professional advice may be needed Flexible, can be customised Counterparty risk Reversible Complex Beneficial rates for both parties Not controlled by exchange Removes FX/Interest Rate risk Last longer then FRA’s (up to 20 years) SWAPS WEEK 16: OPTIONS 1. What is option? 2. Terminology of option. 3. Profit diagrams of basic option positions. LEARNING OUTCOMES  Options are a financial derivative sold by an option writer to an option buyer. The contract offers the buyer the right, but not the obligation, to buy (call option) or sell (put option) the underlying asset at an agreed-upon price during a certain period of time or on a specific date.  All hedges so far give commitment. Options, instead, give the ‘right’ to transact but not the ‘obligation’ They operate more like an insurance policy than a hedge as they will only be ‘exercised’ if the benefit is there.   OPTIONS Put (right to sell asset @ fixed price)  Call (right to buy asset @ fixed price) ◦ Eg. Coupon; ticket price  ‘Long’ a ... (have bought an option) Buyer  ‘Short’ a ... (have sold an option) Seller   Strike Price/Exercise price - The agreed upon price is called the strike price. OPTION TERMINOLOGY  ‘In’, ‘Out of’ or ‘At the money’ Call option £100/stock strike price in 3 mths t=3mths £90 out of the money £110 in the money Put option £100/stock strike price in 3 mths t=3mths £90 in the money £110 out of the money Intrinsic Value − in the money  American & European (Bermudan & Canary!)  OPTION TERMINOLOGY Profit Strike price Terminal price of underlying assets Intercepts? Premium PROFIT DIAGRAM – LONG CALL Strike price PROFIT DIAGRAM – SHORT CALL Strike price PROFIT DIAGRAM – LONG PUT Strike price PROFIT DIAGRAM – SHORT PUT WEEK 17: OPTIONS (FX) 1. What is FX option? 2. How to hedge using FX option? LEARNING OUTCOMES Foreign exchange option (commonly shortened to just FX option or currency option) is a derivative financial instrument that gives the right but not the obligation to exchange money denominated in one currency into another currency at a preagreed exchange rate on a specified date. FX option Strike Calls (c/£) Price Buy £ ($/£) Mar Apr May Puts (c/£) Sell £ Mar Apr May 1.425 2.29 2.32 2.49 0.02 0.14 0.45 1.450 1.31 1.47 1.84 0.03 0.48 0.98 1.475 0.83 1.05 1.42 0.13 1.20 1.84 @ this ‘price’ OPTION QUOTATION 1. 2. 3. 4. 5. 6. Contract Date Put or Call Strike Price and Premium Convert Premium @ S0 Exercise option? Net Outcome STEPS No right answer  The more expensive options give better coverage, e.g. Full cover vs 3rd-party insurance on your car  Decision could be linked to your liquidity position.  WHICH STRIKE PRICE IS BEST? A UK company buys goods from the US for $2,500,000 payable in April  The S0 is $1.4850/£ and the company is concerned that the $ might strengthen  Using table on previous slide hedge at $1.4750/£.   Calculate the sterling cost should the spot rate in April be: ◦ $1.5100/£ ◦ $1.4600/£ OPTION EXAMPLE A UK company sells goods to the US for $1,500,000 payable in April. The S0 is $1.4234 - $1.4378/£ and the company is concerned that the $ might weaken  Using table on previous slide hedge at $1.4250/£.   Calculate the sterling cost should the spot rate in April be: ◦ $1.4100/£ ◦ $1.4600/£ FURTHER EXAMPLE WEEK 18: OPTIONS (INTEREST RATES)  1. What is interest rate option?  2. Quotation of interest rate option.  3. How to use interest rate option to hedge?  4. How to generate a collar? LEARNING OUTCOMES Interest rate options give buyers the right, but not the obligation, to synthetically pay (in the case of a cap) or receive (in the case of a floor) a predetermined interest rate (the strike price) over an agreed period.  Exchange traded insurance instrument  Calls (cap on interest payable – borrower)  Puts (floor on interest received – lender)   The ‘right, but not obligation’ to use an option INTEREST RATE OPTIONS Strike Calls (%) Price Borrow Cash Mar June Sept Puts (%) Lend Cash Mar June Sept 93.50 0.46 0.53 0.63 0.14 0.92 1.62 93.00 0.25 0.34 0.41 0.28 1.15 1.85 @ this ‘price’ 92.50 0.11 0.17 0.23 0.49 1.39 2.10 OPTION QUOTATION Y plc wants to borrow £3m fixed in March for 9 months and wants to protect against rates rising above 7%  It is the 12th of January and interest rates are currently 5.5%  Illustrate the impact of the hedge if interest rates at close out are:  ◦ 7.4% ◦ 5.1% OPTION EXAMPLE IN Cap OUT Floor IN CAPS, FLOORS AND COLLARS INCREASE IN... CALL PRICE PUT PRICE ? ? Share/Commodity price Exercise price Volatility Time to Expiry Risk-free rate of Return DETERMINANTS OF OPTION PRICES WEEK 19: OPTION TRADING STRATEGIES  1. Get to know some basic option trading strategies  2. Understand spread and combination  3. Be able to draw payoff diagram for spread and combination positions  4. Be able to justify which strategy should be applied with respect of stock changes. LEARNING OUTCOME One of the most interesting characteristics of am option is that it can be combined with its underlying assets or other options to produce a wide variety of alternative strategies.  Want to receive (some) benefit or mitigate (some) loss  Reduces overall cost  WHY? Take a position in the option and the underlying asset 2. Take a position in 2 or more options of the same type (A spread) 3. Combination: Take a position in a mixture of calls & puts (A combination) 1. THREE GENERAL STRATEGIES Profit Profit K K ST ST (a) (b) Profit Profit K K ST (c) (d) 1. OPTION & THE UNDERLYING ST Profit ST K1 K2 Anticipating Price Increase 2. ‘BULL’ SPREAD USING CALLS Profit K1 K2 ST Anticipating Price Increase 3. ‘BULL’ SPREAD USING PUTS Profit Anticipating Price Decrease K1 K2 4. ‘BEAR’ SPREAD USING PUTS ST Profit Anticipating Price Decrease K1 K2 5. ‘BEAR’ SPREAD USING CALLS ST Profit K1 K2 K3 ST Anticipating Stable Price 6. ‘BUTTERFLY’ SPREAD USING CALLS Profit K1 K2 K3 ST Anticipating Stable Price 7. ‘BUTTERFLY’ SPREAD USING PUTS Profit K ST Anticipating anything but a Stable Price 8. A ‘STRADDLE’ COMBINATION Profit Profit K ST Strip Long 1 call and 2 puts Anticipate a higher chance of price drop 3. ‘STRIP’ & ‘STRAP’ K ST Strap Long 2 calls and 1 put Anticipate a higher chance of price increase  1. What is call-put parity?  2. Be able to prove Call-put parity WEEK 20: OPTION PRICING – CALL/PUT PARITY  1. What is call-put parity?  2. Be able to prove Call-put parity via payoff table.  3. Be able to calculate call or our option price using call-put parity LEARNING OUTCOMES  Call-Put Parity defines a relationship between the price of a European call option (C) and European put option (P) , both with the identical strike price (K) and expiry (R). Call-put parity  Call: ◦ C = max (S - K, 0)  Put: ◦ P = max (K - S, 0) You hold a call option on X plc where the current share price is £12.45 and the options strike price is £12.25. Is it of any value?  What if the option was a put?  OPTION VALUE  Assuming ◦ Portfolio 1: Long asset, long put option ◦ Portfolio 2: Long zero coupon bond (of redemption value K), long call option  In a frictionless world these would have equal value, therefore: PARITY Pay off table for Portfolio 1 & 2, must consider a range of St values Portfolio 1 Portfolio 2 PV(Portfolio 1) S0 + P S0 + P St>K StP if S>K and vice versa OPTION PRICES WEEK 21: OPTION PRICING - BINOMIAL  1. what is binomial option pricing model?  2. The main assumption of it?  3. Be able to calculate call and put option price using binomial option pricing model. LEARNING OUTCOMES The binomial option pricing model is more of a computational procedure to determine the exact option price directly from the factors that influence it.  It assumes a perfectly efficient market and takes a risk-neutral approach to valuate.  It assumes that underlying assets prices can only either increase or decrease with time until the option expires worthless.  A share price is currently £20, and an risk free return of 12% is anticipated.  In three months it will be either £22 or £18.18 (50:50)  Share Price = £22 Share price = £20 Share Price = £18.18 BINOMIAL MODEL  A 3-month call option on the share has a strike price of 21. Share Price = £22 Option Value = £1 Share price = £20 Option Price=? Profit Share Price = £18.18 Option Value = £0 CALL OPTION  Consider the Portfolio: long x shares & short 1 call option 22.x – 1 18.18x - 0  Portfolio is riskless (or has constant profit, ie. s =0) when 22x – 1 = 18.18x or x = 0.262 CONSTRUCT A RISKFREE PORTFOLIO  The riskless portfolio is: long 0.262 shares short 1 call option The value of the portfolio in 3 months is 22  0.262 – 1 = 4.764  The value of the portfolio today is 4.764 .e-0.12x0.25= 4.623  VALUE THE PORTFOLIO  The portfolio that is worth 4.623  The value of the shares is 5.24 (= 0.262  20 )  The value of the option is therefore 5.24-C0(present value of the call option)=4.623 0.617 (= 5.24 – 4.623 ) VALUING A CALL OPTION A share price is currently £10, free-risk return 3%  In three months it will be either £12 or £8  Call Option Strike Price is £9.50  Option price?  YOUR GO!  1st Solution: generate portfolio: long assets & long put option;  2nd Solution: Call-Put parity S+P=C+K∙e-rn PUT OPTIONS? WEEK 23: OPTION PRICING - BLACK SCHOLES  1. What is Black Scholes Model?  2. The assumption of Black Scholes Model?  3. Be able to apply Black Scholes Model to price European options. LEARNING OUTCOMES  Black-Scholes is a pricing model used to determine the fair price or theoretical value for a call or a put option based on six variables such as volatility, type of option, underlying stock price, time, strike price, and risk-free rate. BLACK SCHOLES MODEL 1. Asset prices follow ‘geometric Brownian motion’ 1. Random 2. No gaps or jumps Risk free rate is constant 3. No dividends from asset during the life of the option 4. Options are European style 5. Assumes Call/Put parity 2. BLACK SCHOLES ASSUMPTIONS  Remember: C = S + P – Ke-rt P = Ke-rt + C – S  When the intrinsic value of C>0, P=0 and vice versa leaving: C = S – Ke-rt P = Ke-rt – S OPTION PRICES 𝑪 = 𝑵 𝒅𝟏 𝑺 − 𝑵 𝒅𝟐 𝑲𝒆−𝒓𝒕 𝑷 = 𝑵 −𝒅𝟐 𝑲𝒆−𝒓𝒕 − 𝑵 −𝒅𝟏 𝑺 𝑆0 ln⁡ ( ) 𝜎√𝑡 −𝑟𝑡 𝐾. 𝑒 𝑑1 = + 2 𝜎√𝑡 𝑑2 = 𝑑1 − 𝜎√𝑡 BLACK SCHOLES FORMULAE  Where: N(d1 or d2) = cumulative probability of d1/d2 occurring (using a normal distribution table) t = Time to maturity S = Spot price K = Strike price r = Risk free rate s = Volatility of asset price BLACK SCHOLES FORMULAE Suppose X ∼ N(0, 1)  N(d1) is the probability that X is smaller than d1.  0.45 0.4 0.35 0.3 0.25 0.2 0.15 0.1 0.05 0 -4 -3 -2 -1 d1 0 Normal Distribution 1 2 3 4 X 1. 2. 3. 4. 5. Compute d1 Compute d2 Compute N(d1) and N(-d1) Compute N(d2) and N(-d2) Compute C and P USING IT...  S = £20 K = £22 t = 3 months r = 4% s = 0.12  C? P?     EXAMPLE WEEK 24: THE ‘GREEKS’  What is the purpose of Greek letter in options?  Be able to tell the meaning of several first order and second order Greeks. LEARNING OUTCOMES Many options traders rely on the "Greeks" to evaluate option positions and to determine option sensitivity.  The Greeks are a collection of statistical values that measure the risk involved in an options contract in relation to certain underlying variables. Popular Greeks include Delta, Vega, and Theta. Rho is another value you may encounter.  Sensitivity is the magnitude of a financial instrument's reaction to changes in underlying factors. Revenue 10 units @ £4 each Materials 2kg/unit @ £0.5/kg Labour 0.5hrs/unit @ £4/hr PROFIT SENSITIVITY £40 (£10) (£20) £10  The degree to which a input or parameter influences the price of an option  1st order ‘Greeks’: ◦ ◦ ◦ ◦ Delta (∆) Theta (Θ) Vega (ν) Rho (ρ) - Asset price - Passage of time - Volatility of asset price - rf SENSITIVITY Delta (D) is the rate of change of the option price with respect to the underlying asset.  It is the slope of the curve that relates the option price to the underlying assets price  Option price Slope = D B DELTA A Stock price     Values between 0 and 1 for a long call/short put Values between 0 and -1 for a long put/short call A value of 1 means a £1 increase in Asset price is matched by a £1 increase in option value, therefore an option with Δ=1 is equivalent to owning a share. Conversely, a value of 0 means a £1 increase in Asset price has no influence on option value option value, therefore an option with Δ=0 is equivalent to owning nothing. DELTA ∆𝑐𝑎𝑙𝑙 − ∆𝑝𝑢𝑡 = 1 A portfolio Delta close to -1 or 1 is very sensitive to asset value so is more volatile and therefore risky.  Delta hedging is where options are selected which attempt to maintain a neutral portfolio delta.  DELTA HEDGING Suppose the delta of a call option is 0.6. When the stock price increases by a small amount, the option price increases by about 60% of that amount.  Trader would be hedged with the position: ◦ short 1000 options ◦ buy 600 shares  Gain/loss on the option position is offset by loss/gain on stock position  Delta changes as stock price changes and time passes  Hedge position must therefore be rebalanced  DELTA Hedging      Theta (Q) is the rate of change of the value of the portfolio with respect to the passage of time Q = ∆Portfolio ∆Time The theta of a call or put is usually negative. This means that, if time passes with the price of the underlying asset and its volatility remaining the same, the value of a long call or put option declines. This is because, as time passes, the option tends to become less valuable. THETA   Vega (n) is the rate of change of the value of a derivative with respect to volatility of the underlying asset Delta is sensitivity to asset price change, Vega also includes the tendency to change. VEGA  Rho is the rate of change of the value of a derivative with respect to the risk free interest rate  Least used of 1st order Greeks  Expressed as the price change for a 1% change in rf RHO Gamma (G) is the rate of change of delta (D) with respect to the price of the underlying asset.  If Gamma is small, delta change slowly with the changes of assets price. Then the adjustments to keep a portfolio dealt neutral need to be made only relatively infrequently.  If Gamma is highly negative or positive, delta is very sensitive to the price of underlying assets. It is then quite risky to leave a delta-neutral portfolio unchanged for any length of time.  2nd ORDER GREEKS WEEKS 25: VALUE AT RISK (1)  1. What is Value of Risk?  2. Be able to calculate VaR of single asset. LEARNING OUTCOMES Value at risk is a statistic that measures and quantifies the level of financial risk within a firm, portfolio or position over a specific time frame.  “What loss level is such that we are x% confident it will not be exceeded in n business days?” (10-day 99% VaR)  VaR is the loss level that will not be exceeded with a specified probability  Value at Risk It captures an important aspect of risk in a single number  It is easy to understand  It asks the simple question: “How bad can things get?”  USES OF VaR 𝑥 34% 1% z=2.33𝜎 z=1𝜎 X follow a normal distribution X∼ N(𝜇,𝜎) 𝑧= 𝜇−𝑥 ; 𝜎 𝜇 − 𝑥 is 𝑉𝑎𝑅 = 𝑧 ∙ 𝜎, 𝑧 is determined by confidence level, 𝜎 is determined by time length and daily volatility. How to calculate VaR In option pricing we express volatility as volatility per year  In VaR calculations we express volatility as volatility per day  s day = s year 252 s n day = s day  n DAILY VOLATILITIES We have a position worth $10 million in Microsoft shares  The volatility of Microsoft is 2% per day (about 32% per year)  We use n = 10 and x = 99 (Number of day / time length 10 days; confidence level 99%) 𝑉𝑎𝑅 = z ∙ 𝜎 = 𝑧99% ∙ 𝜎10𝑑𝑎𝑦𝑠  MICROSOFT EXAMPLE The standard deviation of the change in the portfolio in 1 day is $200,000  The standard deviation of the change in 10 days is  200,000 10 = $632,456 MICROSOFT EXAMPLE cont. We assume that the expected change in the value of the portfolio is zero (This is OK for short time periods)  We assume that the change in the value of the portfolio is normally distributed  Since N(–2.33)=0.01 (one-sided test), the VaR is  2.33  632,456 = $1,473,621 MICROSOFT EXAMPLE cont. WEEKS 26: VALUE AT RISK (2)  1. Be able to calculate VaR for a portfolio/multiple assets  2. Be able to calculate benefits of diversification. LEARNING OUTCOMES One goes up, the other does what?  Covariance and Correlation are two mathematical concepts measures the dependency between two random variables.  Covariance is nothing but a measure of correlation. On the contrary, correlation refers to the scaled form of covariance.  ASSET CORRELATION 𝐶𝑜𝑣(𝑎,𝑏)  𝑅𝑎𝑏 = 𝜌 = 𝜎𝑎 𝜎𝑏 1  𝐶𝑜𝑣 𝑎, 𝑏 = σ(𝑎 𝑛  − 𝐸 𝑎 )(𝑏 − 𝐸 𝑏 ) The value of correlation takes place between -1 and +1. Conversely, the value of covariance lies between -∞ and +∞. ASSET CORRELATION Assume volatility/standard deviation of asset x is 𝜎𝑥 , volatility/standard deviation of asset y is 𝜎𝑦, and correlation between x and y is 𝜌, then the volatility of portfolio containing x and y is shown as the formula below: s X +Y = s + s + 2 s X s Y 2 X Portfolio Volatility 2 Y s X +Y = s X2 + s Y2 + 2s X s Y If 𝜌 = 1, 𝜎𝑋+𝑌 = Therefore, 𝜎𝑋2 + 𝜎𝑌2 + 2𝜎𝑋 𝜎𝑌 = 𝜎𝑋 + 𝜎𝑌 ; 𝜎𝑋+𝑌 ≤ 𝜎𝑋 + 𝜎𝑌 Portfolio Volatility Consider a position of $5 million in AT&T  The daily volatility of AT&T is 1% (approx 16% per year)  The σ per 10 days is   The VaR is 5m 1%  10 = $158,144 158,114  2.33 = $368,405 AT&T EXAMPLE Now consider a portfolio consisting of both Microsoft and AT&T  Suppose that the correlation between the returns is 0.3   In this case sX = 200,000 and sY = 50,000 and  = 0.3. The standard deviation of the change in the portfolio value in one day is therefore 220,227 PORTFOLIO  The 10-day 99% VaR for the portfolio is 220,227  10  2.33 = $1,622,657  The benefits of diversification are: (1,473,621 + 368,405) – 1,622,657 = $219,369  What if the  was -0.3? VaR FOR PORTFOLIO Daily Volatility ρ  Asset A Asset B Asset C Asset D Asset E 1.8% 0.9% 2.5% 1.5% 4.1% 0.3 -0.1 0.6 -0.7 If you hold a £100k share in Asset A and are looking to invest £50k in a second asset which one should you select? (Calculate the benefit of diversification for each)  What if a 3rd asset was now wanted (another £50k) PORTFOLIO CONSTRUCTION WEEK 27: REVISION     A UK company sells goods to the US for $500,000 receivable in April. The CSR is $1.4450/£ and the company is concerned that the $ might weaken and would like to hedge exchange rate at $1.450/£. Calculate the sterling cost should the spot rate in April be: Q1: $1.4300/£ Q2: $1.4600/£ EXCHANGE RATE OPTION For the following option hedge strategies accurately draw the payoff diagram and complete a payoff table  1. Bull spread using Puts  2. Butterfly spread using calls  OPTION STRATEGY  You currently have a £5m holding in X plc and are considering purchasing a £3m holding in Y plc for your portfolio, the details regarding these two shares are as below:   σx = 7% σy = 5% ρxy = -0.25  𝜎𝑎2 + 𝜎𝑏2 + 𝜌𝑎𝑏 . 𝜎𝑎 . 𝜎𝑏  𝜎𝑝 =  What is the benefit of diversification based on 10 days VaR at 99% confidence level? VAR Strike Price = £11.50, in 3 months  rf = 7%PARITY  Share Price = £14 Share price = £12 Share Price = £8 BINOMIAL MODEL There are two (2) questions, worth 50 marks each. Answer BOTH questions. No formulae or tables are provided. Maximum word count is listed against each question part where applicable. This does not include any calculations. Question 1 – Interest Rate hedging Trader Mill Ltd requires a short-term loan to improve liquidity and anticipate that they will need to borrow €5.6m for six months from the 1st of August (it is now the 1st of April). Current interest rate on the market So is 4.37%. The Finance Director has gathered information regarding possible hedges against an interest rate increase: (a) FRAs are available at a rate of 5%. What would the outcome of the hedge be if, by the 1st August, the interest rate had moved to 3.5%? (8 marks) (b) If FRAs are available at a rate of 5%, what would the outcome of the hedge be if, by the 1st August, the interest rate had moved to 5.5%? (7 marks) (c) Current Future price is 96.5 and the underlying bond size is €125K. In 4 month time, the interest rate So is 6.5% and future rate is 94. What would be the outcome of the future hedge? (10 marks) The Finance Director also consider to hedge the borrowing with interest collar, given the information in the table below. Strike Price Calls (%) Puts (%) Mar June Sept Mar June Sept 93.50 0.46 0.53 0.63 0.14 0.92 1.62 93.00 0.25 0.34 0.41 0.28 1.15 1.85 92.50 0.11 0.17 0.23 0.49 1.39 2.10 (a) Describe the construction of an interest rate collar and assess the impact it will have on the interest rate that a borrower may end up paying. (Max word count is 100 words) (10 marks) (b) Use 93.5 as Floor strike price (Kf) and 92.5 as Cap (Kc), Illustrate the outcome of the collar hedge if interest rate at close out is 5.5%. (15 marks) Total 50 marks Question 2 – Option Trading Strategies Elliott Ltd (Elliott) is a financial institution that would like to invest in option trading with share as underlying asset. Trader A of Elliott expects the share price on the market will decrease in future; whereas the trader B believes share price on the market will be quite fluctuated. You are required to: (a) (b) List all option trading strategies can be applied based on Trader A’s opinion. (4 marks) Draw pay-off diagrams for all strategies in question (a). (6 marks) (c) Design and complete pay-off table(s) for all strategies in question (a) (10 marks) (d) List all option trading strategies can be applied based on Trader B’s opinion (6 marks) (e) Draw pay-off diagrams for all strategies in question (d). (9 marks) (f) Design and complete pay-off tables for all strategies in question (d) (15 marks) Total 50 marks EXAMPLES: EXAMPLE 1: 1. Please explain the operation and purpose of a ‘collar’? A collar is simply the combination of a long position in a cap and a short position in a floor. For detailed information, please refer the reading materials on BB. 2. Please explain some of the factors that influence the price of an interest rate option General rule is that any change that will increase the likelihood of an option being exercised and/or increases the possible payouts will increase the price. Strike Price Calls (%) Puts (%) Mar June Sept Mar June Sept 93.50 0.46 0.53 0.63 0.14 0.92 1.62 93.00 0.25 0.34 0.41 0.28 1.15 1.85 92.50 0.11 0.17 0.23 0.49 1.39 2.10 3. Y plc wants to deposit £2m fixed in May for 9 months and wants to protect against rates 6.5%. It is the 12th of January and interest rates are currently 6.25% June put @ 93.50 £2m x 9/12 x 0.0092 = £13,800 (out) (a) 7.25% Not exercise £2m x 9/12 x 0.0725 = £108,750 (in) Less the £13,800 = £94,950 (in) (b) 6.15% £2m x 9/12 x 0.0615 = £92,250 (in) £2m x 9/12 x 0.0035 = £5,250 (in) Less the £13,800 = £83,700 (in) 4. Y plc wants to borrow £2m fixed in May for 9 months and wants to protect against rates increasing above 7%. Assume that Y plc wants to create a collar to reduce the cost of the hedge (use 93 as your Cap K). Illustrate the impact of the hedge if interest rates at close out are: June long call @ 93.00 £2m x 9/12 x 0.0034 = £5,100 (out) June short put @ 93.00 £2m x 9/12 x 0.0115=£17,250 (in) (a) 7.25% Exercise long call, put will be not exercised £2m x 9/12 x 0.0725 = £108,750 (out) £2m x 9/12 x 0.0025 = £3,750 (in) 108,750-3,750+5,100-17,250=92,850 (out) (b) 6.15% Not Exercise long call, put would be exercised. £2m x 9/12 x 0.0615 = £92,250 (out) £2m x 9/12 x 0.0085 = £12,750 (out) 92,250+12,750+5,100-17,250=92,850 (out) EXAMPLE 2: 1. What is the fundamental problem with the Binomial method of option pricing? Two possible prices 2. A share price is currently £4, in six months it will be either £6 or £2.67 and the Option Strike Price is £4.50. If the risk free rate is 8% what is the call option price? Put option price? 6 long asset, short call option 6x – 1.5 = 2.67x, 4 k = 4.5 2.67 (0.45) = £1.20 2.67 £1.20e-8%.0.5 = £1.153 4 (0.45) - C = £1.153 Price = £0.647 to receive 6 long asset, long put option 6x = 2.67x + 1.83, 4 3. x = 0.45 x = 0.5495 k = 4.5 6 (0.5495) = £3.2976 2.67 £3.2976 e-8%.0.5 = £3.1683 4 (0.5495) + P = £3.1683 Price = £0.9703 to pay A share price is currently £5 with a strike price of £6 the anticipated price values are £3.85 or £6.5. (a) What would the call options be priced at if the time period was: • • 6.5 2 months 4 months long asset, short call option 6.5x – 0.5 = 3.85x, 5 k=6 3.85 (0.1887) = £0.7264 3.85 £0.7264.e-8%.2/12 x = 0.1887 = £0.7167 5 (0.1887) -C Price 6.5 = £0.2268 to receive long asset, short call option 6.5x – 0.5 = 3.85x, 5 (b) 4. = £0.7167 x = 0.1887 k=6 3.85 (0.1887) = £0.7264 3.85 £0.7264.e-8%.4/12 = £0.7073 5 (0.1887)- C = £0.7073 Price = £0.2362 to receive Please explain how the change in time period impacted the change in price. As with Q3 but now the option is a put. 6.5 long asset, short call option 6.5x = 3.85x + 2.15, 5 k=6 6.5 (0. 8113) = £5.2735 3.85 £5.2735.e-8%.2/12 5 (0. 8113) = £5.207 +P Price 6.5 long asset, short call option k=6 6.5 (0. 8113) = £5.2735 3.85 £5.2735.e-8%4/12 5 (0. 8113) Price Example 3 : = £5.207 = £1.1472 to receive 6.5x = 3.85x + 2.15, 5 x = 0. 8113 x = 0. 8113 = £5. 1347 +P = £5. 1347 = £1.078 to receive 1. Why would an investor want to construct a hedge with options rather than just take the benefit offered? Cost savings, unsure of actual outcome 2. For the below strategies please draw the diagrams, state what it is the investor is anticipating (in terms of the value of the underlying asset) and how the strategy takes advantage of the anticipated outcome. (a) ‘Bull’ spread using calls (b) ‘Bear’ spread using puts (c) ‘Butterfly’ spread using calls (d) A ‘straddle’ combination (e) A ‘strap’ 
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