A stock has a current price of $100.Assume a CRR-style jump-to-default model in which the volatility is 30%.Let the risk-neutral probability of default in three months be 10%.The 3-month risk-free rate is 2% in continuously-componded and annualized terms.What is the price of a three-month at-the-money put option on this stock in a one-period jump-to-default tree model?

Question

Quizplus · Accepted Answer

The calculations are as follows:
> u=exp(0.3*sqrt(1/4))
> d=1/u
> R=exp(0.02/4)
> lambda=0.10
> q = (R/(1-lambda)-d)/(u-d)
> q
[1] 0.8500507
> put = ((100-100*d)*(1-q)*(1-lambda)+100*lambda)/R
> put
[1] 11.82056

A Stock Has a Current Price of $100