Problem 16.1

A portfolio is currently worth $10 million and has a beta of 1.0. An index is currently standing at 800.

Explain how a put option on the index with a strike of 700 can be used to provide portfolio insurance.

When the index goes down to 700, the value of the portfolio
can be expected to be 10×(700 / 800) = $8.75 million.

(This assumes that the dividend yield on the portfolio equals
the dividend yield on the index.)

Buying put options on 10,000,000/800 = 12,500 times
the index with a strike of 700 therefore provides protection
against a drop in the value of the portfolio below $8.75 million.

If each contract is on 100 times the index a total of
125 contracts would be required.

Problem 16.4.

A currency is currently worth $0.80 and has a volatility of 12%.

The domestic and foreign risk-free interest rates are 6% and 8%, respectively.

Use a two-step binomial tree to value

a) a European four-month call option with a strike price of$0.79 and

b) an American four-month call option with the same strike price.

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In this case  u=1.0502 and  p=0.4538. The tree is shown above.
The value of the option if it is European is $0.0235; the value
of the option if it is American is $0.0250.

Problem 16.18.

An index currently stands at 1,500. European call and put options with a strike price of 1,400 and time to maturity of six months have market prices of 154.00 and 34.25 , respectively.

The six-month risk-free rate is 5%.

What is the implied dividend yield?

The implied dividend yield is the value of q that satisfies
the put-call parity equation.
It is the value of q that solves

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This is 1.99%.

Problem 16.10.

Consider a stock index currently standing at 250. The dividend yield on the index is 4% per annum, and the risk-free rate is 6% per annum. A three-month European call option on the index with astrike price of 245 is currently worth $10. What is the value of a three-month put option on theindex with a strike price of 245?

In this case,

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The put price is 3.84.