a) Today a JPMorgan (JPM) trader buys 100 puts (on a stock) for P = $6...

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a) Today a JPMorgan (JPM) trader buys 100 puts (on a stock) for P = $6 each (K=$100, T=1 year and Ap - 0.5). == The initial stock price is S = $100 and the price falls next day to S=$99, with a new delta of A = -0.6. The risk-free rate is 0.01% per day (3.7% pa). P Required The stock price falls (monotonically) to ST =$70 at maturity of the option, when A, =-1. The JPM trader delta hedges the puts and ends up with debt (ie. bank loan) of $10,010. i) Explain how the JPM trader dynamically hedges over the first two days ii) Explain the outcome at expiration of the option when the JPM trader closes out all her positions - assume i) delivery in the put contract and ii) the put is cash settled. (25%) b) You hold Portfolio-A of options (on the same stock) with a current market value of $2,000. The portfolio delta, gamma and vega are: A = -50, T=-600, A =-400 Required i) "If the stock price falls by $2 (over one day), what is the change in value of portfolio- A? Would you hedge both the delta and gamma risks? ii) If the volatility of the stock increases from 20% to 25% (over one day), what is the change in value of portfolio-A? Would you hedge this risk? The following option (on stock-A) is also available: Option 'Z' which has Az = 0.6, I = 0.04, Az = 16 Z iii) How can you combine options A and Z to give a portfolio which is "gamma neutral"? a) Today a JPMorgan (JPM) trader buys 100 puts (on a stock) for P = $6 each (K=$100, T=1 year and Ap - 0.5). == The initial stock price is S = $100 and the price falls next day to S=$99, with a new delta of A = -0.6. The risk-free rate is 0.01% per day (3.7% pa). P Required The stock price falls (monotonically) to ST =$70 at maturity of the option, when A, =-1. The JPM trader delta hedges the puts and ends up with debt (ie. bank loan) of $10,010. i) Explain how the JPM trader dynamically hedges over the first two days ii) Explain the outcome at expiration of the option when the JPM trader closes out all her positions - assume i) delivery in the put contract and ii) the put is cash settled. (25%) b) You hold Portfolio-A of options (on the same stock) with a current market value of $2,000. The portfolio delta, gamma and vega are: A = -50, T=-600, A =-400 Required i) "If the stock price falls by $2 (over one day), what is the change in value of portfolio- A? Would you hedge both the delta and gamma risks? ii) If the volatility of the stock increases from 20% to 25% (over one day), what is the change in value of portfolio-A? Would you hedge this risk? The following option (on stock-A) is also available: Option 'Z' which has Az = 0.6, I = 0.04, Az = 16 Z iii) How can you combine options A and Z to give a portfolio which is "gamma neutral"?

Answer rating: 100% (QA)

a i The JPM trader dynamically hedges over the first two days by adjusting the number of shares held to maintain a deltaneutral position Delta represents the sensitivity of the option price to changes ... View the full answer