# Write the payoff function for this straddle and zero coupon bonds

**Question description**

Assume that the yields to maturity, continuously compounded, for zero coupon bonds maturing in half a year, one year, and one and half years from now are 0.85%, 0.90%, and 0.97%, respectively. Assume that the current short rate, i.e. the rate on the 6-month bonds, follows a binomial stochastic recombining process such that it either increases or decreases 20% every six months with a 50% probability in either direction at every node. Now consider a risk-free zero coupon bond that pays a par value of $100 at the end of one year from now. As a financial engineer, we are about to value a straddle with a strike price at $99.5928, which matures a year hence. Assume that the underlying asset is the bond maturing in one and half years from now. Write the payoff function for this straddle OR value the derivative based on the interest rate assumptions.

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