APPLICATIONS OF OPTION PRICING
• Valuation of an FDIC guarantee
Bank One’s assets are worth $950 million today. They have a volatility of 10%, and the riskfree rate is 6%. The insured deposits of Bank One will be a sum of $800 million, and the insurance will expire in one year’s time.
a) FDIC provides a guarantee to Bank One that all of its insured deposits will be paid if Bank One is unable to repay those deposits. Compare this guarantee with a put option. In particular specify the following characteristics of the Put.
(i) What is the underlying asset of the put?
(ii) Who writes the put?
(iii) Who owns the put?
(iv) What is the expiration date of the put?
(v) What is the exercise price of the put?
b) Using the Black-Scholes formula compute the price that FDIC should charge for providing the above-mentioned guarantee to Bank One.
• Portfolio Insurance as Put Options
Abacus Associates, a new and highly innovative money managing firm run by two Ex-Tulanians (who took the Finance – II course, but dropped out of school soon after to start this firm) decides to offer the following “Portfolio Insurance” to the endowment fund of the Freeman School. The Freeman School fund is currently worth $32 million and it is invested in a Portfolio of assets that have a variance of 0.0225 (volatility of 15%). Abacus offers to guarantee a return of 5% on the portfolio i.e., if the fund drops below $33.6 million in value at the end of 39 weeks, then Abacus Associates will make-up the difference. (Of course, if the fund does better than 5% then the School gets to keep the proceeds). For your computations assume that the riskfree rate is 6%.
a) Compare this Portfolio Insurance to a Put Option. In particular specify the following characteristics of the Put.
(i) What is the underlying asset of the put?
(ii) Who writes the put?
(iii) Who owns the put?
(iv) What is the expiration date of the put?
(v) What is the exercise price of the put?
(vi) When is the Put “in-the-money”? (i.e., For what range of values of the Portfolio is the put in-the-money?)
b) Using the Black-Scholes formula compute the fair price that Dean McFarland should expect to pay for this insurance.