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Hedging the Sale of a Vanilla Eupopean-Style Call Option on a Dividend-Paying Stock

To discuss this, I will revisit the example illustrated in Table 7.1 and show how the delta-hedging mechanics carried out in Table 7.7 is affected by a dividend paying stock.

As can be seen in Table 7.7, column J illustrates how dividends play the role of reducing the borrowing costs. Running a daily simulation over 5,000 paths, it can be seen that the final result in cell K13 averages to 0 – confirming the theoretical fair value charged for the sale of this option (i.e., premium of $580).

TABLE 7.5 Settlement Associated with a Delta-Hedging Program for Vanilla European-Style Call Option on a Nondividend-Paying Stock (In-The-Money Expiry)

TABLE 7.6 Settlement Associated with a Delta-Hedging Program for Vanilla European-Style Call Option on a Nondividend-Paying Stock (Out-Of-The-Money Expiry)

TABLE 7.7 Settlement Associated with a Delta-Hedging Program for a Vanilla European-Style Call Option on a Dividend-Paying Stock (In-The-Money Expiry)

Hedging the Sale of a Vanilla European-Style Put Option on a Dividend-Paying Stock

Hedging the sale of a put option is philosophically similar to that of the call option that was discussed earlier. The only exception is that to have a riskless portfolio, the hedger would now need to short the shares as opposed to buying the shares.[1] Table 7.8 shows an illustration associated with hedging the sale of the put option when the option finishes in-the-money.

As can be seen in Table 7.8, one big difference between Tables 7.7 and 7.8 is the way the terms in columns E and F are computed. Additionally, in cell Ell, I hard-coded a value of -1 to reflect the fact that the put option finished in-the-money. In the event that the put option finishes out-of-the- money, this would have a value of 0.

  • [1] The implication of this is that in a market where shorting of shares is not allowed, it becomes impossible for one to risk-manage the sale of the put option using delta hedging. In such an instance, the only risk-management strategies available to the hedger are that of taking the risk naked or buying a structurally similar put from another counterparty. As the astute reader will realize, the problem of shorting also exists if the hedger decides to delta-hedge the purchase of a call option.
 
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