Consider two European put options on a dividend paying stock in the Black-Scholes framework. You are given
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Question:
Consider two European put options on a dividend paying stock in the Black-Scholes framework. You are given the following:
i) The stock is currently selling for $70.
ii) The stock pays dividends continuously at a yield of 2%.
iii) The stock's volatility is 25%.
iv) The continuously compounded risk-free interest rate is 3%.
v) Put 1 has a strike of $70, expires in 6 months, and has a gamma of 0.08.
vi) Put 2 has a strike of $60, expires in 1 year, and has a gamma of 0.05.
A market-maker has just sold 100 of Put 1 and wishes to both delta-hedge and gamma-hedge her position using Put 2 and/or the underlying stock. What will be her position in the underlying stock?
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