I work for a financial institution. I have the following portfolio of over-the-counter options on silver....

Transcribed Image Text:

I work for a financial institution. I have the following portfolio of over-the-counter options on silver. Each contract is for 250 ounces of silver. Current position (# contracts) Vega Delta Gamma Call A Short 250 0.60 1.3 1.5 Call B Long 75 0.20 1.8 0.9 Put C Short 100 -0.80 0.4 0.8 Put D Long 50 -0.40 0.6 1.3 (a) What are the delta and vega of my portfolio? (b) My friend is a market maker who has completed several trades in options on silver today. At the end of the trading day, her portfolio has a delta of 800 and a gamma of -2500. She wants to delta-gamma hedge her portfolio against overnight price risk, using a position in spot silver and call B from the table above. What position in the spot asset and put C should she take to gamma and delta hedge her portfolio? (c) You see a new call option on silver. Its maturity is 3 months and strike price $150. The current spot price of the underlying asset is $120 per ounce and the return volatility of silver is 60% per annum. The continuously-compounded risk-free rate is 2% per annum. What are the delta and gamma of this call option, assuming the Black-Scholes-Merton assumptions are satisfied? I work for a financial institution. I have the following portfolio of over-the-counter options on silver. Each contract is for 250 ounces of silver. Current position (# contracts) Vega Delta Gamma Call A Short 250 0.60 1.3 1.5 Call B Long 75 0.20 1.8 0.9 Put C Short 100 -0.80 0.4 0.8 Put D Long 50 -0.40 0.6 1.3 (a) What are the delta and vega of my portfolio? (b) My friend is a market maker who has completed several trades in options on silver today. At the end of the trading day, her portfolio has a delta of 800 and a gamma of -2500. She wants to delta-gamma hedge her portfolio against overnight price risk, using a position in spot silver and call B from the table above. What position in the spot asset and put C should she take to gamma and delta hedge her portfolio? (c) You see a new call option on silver. Its maturity is 3 months and strike price $150. The current spot price of the underlying asset is $120 per ounce and the return volatility of silver is 60% per annum. The continuously-compounded risk-free rate is 2% per annum. What are the delta and gamma of this call option, assuming the Black-Scholes-Merton assumptions are satisfied?