To hedge or not to hedge?!

Pricing options have been scientific and had won the Noble prize for Merton and Scholes for their groundbreaking work. But ask any market-maker or an options trader (vanilla or exotic) the perils of running an options book. The clarity and the scientific approach that accompanies the pricing model suddenly disappear in the wake of hedging the same options book.

Delta hedging sounds like a child’s play: You hedge the Delta exposure by buying or selling of the underlying and thereby flatten your exposure to the underlying and then go to the bank to cash your profits arising from the difference in volatilities of implied and realized. Easy no?! Far from it.

When to hedge (daily, hourly or weekly?), how much to hedge (go with the total delta or take a view?) etc are questions that have no good scientific answers. To make a point we did the following exercise: We sold 100 lots of a 1-Year ATM call priced at 50% and we made the market to realize about 40% of volatility through a series of Monte Carlo simulations. Specifically, we ran 10,000 runs of an MC simulation simulating daily prices of up to 365 days with a volatility of 40% (so, 3650000 computations using multiprocessing). In each of the 10,000 runs, we computed the profit/loss arising from the hedged book (daily hedging at the close). Theoretically, the Vega of the book should have made us USD 400 from letting the options expire after a year after delta-hedging daily at the closes.

After the 3.65 Million computations (365 days of prices simulated for 10000 runs of MC) the average profits that a trader would have been able to capture in this trade is USD 254. Of course, we could do other periodicities and forms of the delta hedging like weekly or twice daily or based on a threshold move of the market (say a Maximum favorable excursion) etc but the fact remains that there is no perfect delta hedging routine that one could take. If you want to hedge better talk to us and we would be glad to help.

Originally published at https://www.linkedin.com.