# python help please

**Question description**

A type-Z option has the following payoff function:

{ K[1+sin(2*pi*St/(K))] if St<K

F(St)=

{K*exp^1-St/(k) if St>=K

1. Write a Python function with the following definition: def f(ST,K):

which calculates the payoff of a type-Z option.

Write a Python function with the following definition:

def plotTypeZPayoff (K,STMax):

which plots the payoff function of the type-Z option as a function of ST for given K. The range of the horizontal axis should be [0,STMax] and vertical axis [0,2.1K]. Include this graph in your written work for the case K = 20,STMax = 100.

2. Write a loop based binomial options pricing function with the definition: def binomOption(payoff ,steps ,T,sigma,S0,r): where payoff is a function of one variable. The variable sigma (σ) is the volatility, √√ related to u and d by u=exp(σ sqrt(δt)) and d=exp(−σ sqrt(δt)). Write a factory function with the definition:

def makeZPayoff(K):

which returns a type-Z payoff function with fixed K.

3. Fix T = 1,r = 0.05,K = 20,S0 = 15,steps = 200. Calculate the value of the type-Z option for σ ∈ {0.01, 0.1, 0.2, 0.3}. Produce a two column table of σ values and the corresponding option values in your written work. Explain why increasing σ increases the value of the option in this example. What do you expect to happen as σ → ∞ and why? If S0 = K, what would be the effect of increasing σ and why?

Fix T = 1,r = 0.05,K = 20,S0 = 15,steps = 200. Produce a graph of the type-Z option’s value at t = 0 as a function of S0 for S0 ∈ [0,100] for each of the following values of σ : {0.01, 0.1, 0.2, 0.3}. Show all four graphs on the same axes and include it in your written work. What effect does increasing volatility have on the price graph and why?

Fix T = 1,r = 0.05,K = 20,S0 = 15,steps = 200 and suppose the option’s value is V0 = 2.0. Write a root finding function to calculate the volatility σ correct to 6 significant figures. Include the result in your written work.

## Tutor Answer

**Quality**

**Communication**

**On Time**

**Value**

Brown University

1271 Tutors

California Institute of Technology

2131 Tutors

Carnegie Mellon University

982 Tutors

Columbia University

1256 Tutors

Dartmouth University

2113 Tutors

Emory University

2279 Tutors

Harvard University

599 Tutors

Massachusetts Institute of Technology

2319 Tutors

New York University

1645 Tutors

Notre Dam University

1911 Tutors

Oklahoma University

2122 Tutors

Pennsylvania State University

932 Tutors

Princeton University

1211 Tutors

Stanford University

983 Tutors

University of California

1282 Tutors

Oxford University

123 Tutors

Yale University

2325 Tutors