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8 Jan 2018

You have just bought an at-the-money call option (N(d1) = 0.5), on ABC stock, with 6 months to expiration. What transaction would you do to delta-hedge this option?

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10 Jan 2018

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Suppose you construct an option hedge by buying a levered position in delta shares of stock and selling one call option. As the share price changes, the option delta changes, and you will need to adjust your hedge. You can minimize the cost of adjustments if changes in the stock price have only a small effect on the option delta. Construct an example to show whether the option delta is likely to vary more if you hedge with an in-the-money option, an at-the-money option, or an out-of-the-money option. Comment on your results.

1) You purchased four WXO 30 call option contracts at a quoted price of $.34. What is your net gain or loss on this investment if the price of WXO is $33.60 on the option expiration date? 2) You wrote ten call option contracts on JIG stock with a strike price of $40 and an option price of $.40. What is your net gain or loss on this investment if the price of JIG is $46.05 on the option expiration date? 3) You currently own a one-year call option on Way-One, Inc. stock. The current stock price is $26.50 and the risk-free rate of return is 4%. Your option has a strike price of $20 and you assume that it will finish in the money. What is the current value of your call option? 4) Three months ago, you purchased a put option on WXX stock with a strike price of $61 and an option price of $.60. The option expires today when the value of WXX stock is $63.50. Ignoring trading costs and taxes, what is your total profit or loss on your investment? 5) Suppose you look in the newspaper and see ABC trading at $50 per share. Calls on ABC with one month to expiration and an exercise price of $45 are trading at $6.50 each. Puts on ABC with one month to expiration and an exercise price of $55 are trading at $3.50 each. Are these prices reasonable? Explain. (Ignore transactions costs.) 6) You sold ten put option contracts on PLT stock with an exercise price of $32.50 and an option price of $1.10. Today, the option expires and the underlying stock is selling for $34.30 a share. Ignoring trading costs and taxes, what is your total profit or loss on this investment?

The option delta (i.e., hedge ratio) for a call on Ajax stock is 0.7, while the delta for the put on Ajax stock is -0.3… You wish to hedge a portfolio of 100,000 shares of Ajax. Recall that the option delta is the change in option price for a $1 increase in its stock.

1. How many call options will you need to write to hedge your portfolio using the option delta as your theoretical basis, given writing calls is your only hedge mechanism?

2. How many put options will you need to acquire to hedge your portfolio using the option delta as your theoretical basis, given acquiring puts is your only hedge mechanism?

3. For these two strategies for managing risk, do they cover downside risk associated with underlier price volatility?

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