Suppose S = $100, r = 8%, σ = 30%, T = 1, and δ = 0. Use the Black-Scholes formula to generate call and put prices with the strikes ranging from $40 to $250, with increments of $5. Compute the implied volatility from these prices by using the formula for the VIX (equation (24.29)). What happens to your estimate if you use strikes that differ by $1 or $10, or strikes that range only from $60 to $200?
Answer to relevant QuestionsExplain why the VIX formula in equation (24.29) overestimates implied volatility if options are American. The following three problems use the Merton jump formula. As a base case, assume S = $100, r = 8%, σ = 30%, T = 1, ...Compute daily volatilities for 1991 through 2004 for IBM, Xerox, and the S&P 500 index. Annualize by multiplying by √ 252. How do your answers compare to those in Problem 24.1? Use the following inputs to compute the price of a European call option: S = $50, K = $100, r = 0.06, σ = 0.30, T = 0.01, δ = 0. a. Verify that the Black-Scholes price is zero. b. Verify that the vega for this option is ...You are going to borrow $250m at a floating rate for 5 years. You wish to protect yourself against borrowing rates greater than 10.5%. Using each tree, what is the price of a 5-year interest rate cap? (Assume that the cap ...Suppose the yield curve is flat at 6%. Consider a 4-year 5%-coupon bond and an 8-year 7%-coupon bond. All coupons are annual. a. What are the prices and durations of both bonds? b. Consider buying one 4-year bond and ...
Post your question