GREEKS

Impact of delta and gamma

Question 1

Suppose a stock is currently trading at $47, for which there is a FEB 50 Call option selling for $2.0 with a Delta = 0.4 and a Gamma = 0.1.

REQUIRED:

(a) Calculate the adjusted Delta if the stock price

(i) moves up by $1 to $48, and

(ii) moves downwards by $1 to $46.

(b) Calculate the new price of the option following (i) and (ii) above.

Question 2

You have an underlying futures contract at 200 and the strike is 200. The option price is $7.50. The options Delta is 50 and the options Gamma is 3.

REQUIRED:

(a) Determine the change in Delta if the underlying changes

(i) from $200 to $205 and

(ii) from $200 to $195.

(b) Calculate the new price of the option following (i) and (ii) above

Vega and price change

Question 3

A stock is trading at $46.0 in May and a JUN 50 Call on the stock is trading for $2.0. Assume that the Vega of the option is 0.15 and that the underlying stock volatility is 25%.

Required:

Calculate the change in the option price if

(i) the underlying volatility increases by 1% to 26%,

(ii) the underlying volatility decreases by 2% to 23%,

The Greeks in combination

Question 4

Suppose we have the underlying futures price for an index as $980, for which the $1000 strike Call with 42 days to expiration is priced at $12.0. Suppose the volatility of the futures price at $980 is 15%, and for the 1000 Call, we have: Delta = 0.36 (36); Gamma = 0.0080 (0.80); Theta = 0.23; and Vega = 1.25. The risk-free rate is 1.0% per year. Suppose the market goes to $1000 (up $20) in 2 weeks and volatility for the futures drops to 14%.

Required:

(a) Determine the outcome price (premium) for the option with reference to the Greeks.

(b) Compare your answer in (a) above with the premium price determined by a Black-Scholes calculator