# Question

Covered call writers often plan to buy back the written call if the stock price drops sufficiently. The logic is that the written call at that point has little “upside,” and, if the stock recovers, the position could sustain a loss from the written call.

a. Explain in general how this buy-back strategy could be implemented using barrier options.

b. Suppose S = $50, σ = 0.3, r = 0.08, t = 1, and δ = 0. The premium of a written call with a $50 strike is $7.856. We intend to buy the option back if the stock hits $45. What is the net premium of this strategy?

A European lookback call at maturity pays ST− ST . A European lookback put at maturity pays ST− ST . (Recall that ST and ST are the maximum and minimum prices over the life of the option.) Here is a formula that can be used to value both options:

where

The value of a lookback call is obtained by setting ˜St = ST andω = 1. The value of a lookback put is obtained by setting ˜St = ST and ω=−1.

a. Explain in general how this buy-back strategy could be implemented using barrier options.

b. Suppose S = $50, σ = 0.3, r = 0.08, t = 1, and δ = 0. The premium of a written call with a $50 strike is $7.856. We intend to buy the option back if the stock hits $45. What is the net premium of this strategy?

A European lookback call at maturity pays ST− ST . A European lookback put at maturity pays ST− ST . (Recall that ST and ST are the maximum and minimum prices over the life of the option.) Here is a formula that can be used to value both options:

where

The value of a lookback call is obtained by setting ˜St = ST andω = 1. The value of a lookback put is obtained by setting ˜St = ST and ω=−1.

## Answer to relevant Questions

For the lookback call: a. What is the value of a lookback call as ST approaches zero? Verify that the formula gives you the same answer. b. Verify that at maturity the value of the call is ST − ST . A barrier COD option is like a COD except that payment for the option occurs whenever a barrier is struck. Price a barrier COD put for the same values as in the previous problem, with a barrier of $95 and a strike of $90. ...In this problem we use the lognormal approximation (see equation (11.14)) to draw one-step binomial trees from the perspective of a yen-based investor. Use the information in Table 23.4. a. Construct a one-step tree for the ...Using the Merton jump formula, generate an implied volatility plot for K = 50, 55, . . . 150. a. How is the implied volatility plot affected by changing αJ to−0.40 or−0.10? b. How is the implied volatility plot affected ...Use the following inputs to compute the price of a European call option: S = $100, K = $50, r = 0.06, σ = 0.30, T = 0.01, δ = 0. a. Verify that the Black - Scholes price is $50.0299. b. Verify that the vega for this option ...Post your question

0