Options and Interest Rate Derivatives
SHORT HISTORY OF OPTION PRICING
Stock options in general have been well studied since before the October 19, 1987, Black Monday debacle, when the Dow Jones Industrial Average fell 22.61 percent, markets in Hong Kong fell 45.5 percent, and Australia fell 41.8 percent; by October’s end the contagion had swept the developed world extensively. Later this crisis was diagnosed as being due to program traders, or “algos” as they are now called, using synthetic portfolio insurance, but this is still disputed somewhat. The father of portfolio insurance, Mark Rubinstein (also an inventor of the Cox-Ross-Rubinstein binomial option pricing model), had issued several papers recounting the role of portfolio insurance in the crash both right after and a decade later. He said that any investors who reduced their holdings of stock, shorted stock, covered long futures positions, or increased open sold futures positions on October 19 contributed to the crash.
The concept of portfolio insurance of course involves inverting the Black-Scholes arbitrage argument that states an equity call option can be perfectly hedged by a short stock sale and in so doing yields the riskless rate, which is simply:
Long call option – Stock = Riskless rate
You can easily rearrange this to be:
Long call option = Stock + Riskless rate
So, alternatively, by dynamically hedging a stock with a risk-free ...