I work for a financial institution. I have the following portfolio of over-the-counter options on platinum. Each contract is for 1 ounce of platinum.

Call A Call B Put C Put D

(a) (b)

(c)

Current position (# contracts) Long 1,000 Short 500

Long 2,000 Short 800

Delta Gamma Vega

0.50 1.7 1.8 0.80 1.1 0.2 -0.40 1.3 0.7 -0.70 0.9 2.2

What are the delta and gamma of my portfolio?

My friend is a market maker who has completed a number of trades in options on platinum today. At the end of the trading day, her portfolio has a delta of 300 and a gamma of 5000. She wants to delta-gamma hedge her portfolio against overnight price risk, using a position in spot platinum and put D from the table above. What position in the spot asset and put D should she take to gamma and delta hedge her portfolio?

You see a new call option on platinum. Its maturity is 3 months and strike price is $36. The current spot price of the underlying asset is $37 per ounce and the volatility is 25% per annum. The continuously-compounded risk-free rate is 1% per annum. What are the delta and gamma of the call option, assuming the Black-Scholes- Merton assumptions are satisfied?