Problem 4. (15 points) On October 1, a broker wrote 30 European put options with expiry 2 months and strike price $20 on a stock that was also selling for $20. The broker used Black-Scholes to price them assuming an annual volatility of 10% and an annual risk-free interest rate of 0.5%. (a) Today December 1 (at expiry) the stock is selling at $19. If the broker did not hedge, what is the value of the unhedged portfolio (at expiry)? (b) Perform a monthly Delta-neutral hedging strategy (i.e. times t = 0, t = one month and t = 2 months) and compute the value of the Delta-neutral portfolio today (expiry t = 2 months). The stock price on November 1 was $20.5. (c) Consider the Black-Scholes formula for the price of a put option P(t, S, E) as a function of the volatility and call it P(o). Compute the limit lim P(o) and give a financial meaning to that limit. 0 +0+ Problem 4. (15 points) On October 1, a broker wrote 30 European put options with expiry 2 months and strike price $20 on a stock that was also selling for $20. The broker used Black-Scholes to price them assuming an annual volatility of 10% and an annual risk-free interest rate of 0.5%. (a) Today December 1 (at expiry) the stock is selling at $19. If the broker did not hedge, what is the value of the unhedged portfolio (at expiry)? (b) Perform a monthly Delta-neutral hedging strategy (i.e. times t = 0, t = one month and t = 2 months) and compute the value of the Delta-neutral portfolio today (expiry t = 2 months). The stock price on November 1 was $20.5. (c) Consider the Black-Scholes formula for the price of a put option P(t, S, E) as a function of the volatility and call it P(o). Compute the limit lim P(o) and give a financial meaning to that limit. 0 +0+