Conduct a delta hedge similar to that in Section 5.4.3. In one case assume the stock price increases modestly over the 42 days until expiration. In another, generate a GRW 42 day price sequence.

Data given in Section 5.4.3

Data given in Figure 5.8

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The repair for naked put and call selling is covered calls and protective puts. Covered call writing consists of selling a call on a stock and buying stock in the amount to cover it, 100 shares per contract. Its dual is selling a put and shorting stock to cover it. The payoff diagrams are shown in Fig. 5.8. Although these trades have the same payoff charts as do naked puts and calls, there is a very big difference - the stock purchase occurs up front. Consider the covered call. First the stock is purchased and then the call is sold (or better yet, the trade is made atomically, i.e. as one trade). If the stock experiences an unexpected increase, the stock is already in hand to cover the exercise. If instead the stock price dramatically falls, possibly even to zero, no additional monies are required. This is not the case for a naked put where the money to fulfill the exercise must be forthcoming at expiration. Covered calls are widely used for generating income. If one already owns the stock, and this is where the risk originates, then selling calls on it produces an income stream so long as the stock price finishes below the strike price at expiration. The downside to the strategy occurs when the stock makes a run up. Then the trader only participates to the extent of the strike price and loses the stock upon exercise. Therefore covered calls are a good strategy for generating income on a stock very unlikely to lose value and not gain much in value either.