Consider a Black-Scholes-Merton model with r=0.1, T=0.5 years, S(0)=100. Suppose the Black-Scholes price of the digital option that pays one dollar if S(T)≥100 and zero otherwise, is equal to 0.581534.

Question

Enter the value of volatility σ (hint: it is one of the values 0.1,0.2,…,0.9,1.0) :

correct
0.2

Enter the risk-neutral probability that the option will be in the money:

correct
0.61135

Answer 1

You take a short position in one European put option contract, with strike price 100 and maturity six months, on a stock that is trading at 100. The annual volatility of the stock is constant and equal to 25%. The dividend rate is zero. The annual (continuously compounded) risk-free interest rate is constant and equal to 5%. Suppose that you sold the option at a premium of 6% over the Black-Scholes price, that is, for 1.06 times the Black-Scholes price. You hedge your portfolio with the underlying stock and the risk-free asset. The hedge is rebalanced monthly. After two months the portfolio is liquidated (you buy the option and undo the hedge).

Enter the final overall profit or loss, if the price of the stock is 101 at the end of the first month and 99 at the end of the second month, and assume that the option is traded at exactly the Black-Scholes price at the end of the first month and at the end of the second month

Answer 2

I have this variation, please help:

Consider a Black-Scholes-Merton model with r=0.1, T=1 years, S(0)=100. Suppose the Black-Scholes price of the digital option that pays one dollar if S(T)≥100 and zero otherwise, is equal to 0.51823.

Enter the value of volatility σ (hint: it is one of the values 0.1,0.2,…,0.9,1.0) :


Enter the risk-neutral probability that the option will be in the money: