# payoff function straddle

**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.

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