Homework answers / question archive / A) The stock of the XYZ company trades at $100, and you owe 1,000 shares, as well as 500 call options with a strike of $110 expiring in 6 months, as well as 950 put options expiring in 3 months and with a strike of $85

A) The stock of the XYZ company trades at $100, and you owe 1,000 shares, as well as 500 call options with a strike of $110 expiring in 6 months, as well as 950 put options expiring in 3 months and with a strike of $85

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A) The stock of the XYZ company trades at $100, and you owe 1,000 shares, as well as 500 call options with a strike of $110 expiring in 6 months, as well as 950 put options expiring in 3 months and with a strike of $85. The riskfree rate is equal to zero, and the volatility of XYZ is 25% per year. All options are European and the stock pays no dividends.

1.(20p) what is the value of your portfolio?

2.(20 p) explain how you can delta hedge your portfolio using 6-month call options with a strike of $110. What is the value of the delta hedged portfolio?

3.(20 p) after you delta hedged, the stock price increases by $2. What is the value of your portfolio after the sudden price increase?

4.(20p) assume that after you delta hedged, the volatility of XYZ goes up to 30%. What is the change in value for the hedged portfolio? What would be the change in value if you did not delta hedged?

B. (20 p) Assume that you owe 50 shares of the company XYZ mentioned in problem A. You want to buy insurance against drops in price that are more severe than -30% and you buy 50 6-month puts with the appropriate strike (what is this strike?). However you have no cash, and you wanna sell call options in order to buy these puts. If you want to sell 50 calls, what strike should they have? If you wanna sell 100 calls, what strike should these ones have to finance your puts purchase?

C. ( 20p) Assume that economic conditions are such that market volatility is very low and we are looking for extra cash. One idea is to sell out of the money puts, and hope the market will not fall.

1. Explain how this strategy makes money;
2. Argue why we should NOT implement this strategy.