How do we use option price models (like Black-Scholes Model) to make money in practice?

Question

In quantitative finance, we know we have a lot of option price models such as geometric Brownian motion model (Black-Scholes models), stochastic volatility model (Heston), jump diffusion models and so on, my question is how can we use these models to make money in practice?

My comments: Because we can read option price from the market, by these models (Black-Scholes), we can get the implied volatility, then we may use this implied volatility to compute other exotic option price, then we can make money by selling/buying this exotic option as a market maker, is this the only way to make money?

For stocks, we know that if we have a better model to predict future stock prices, then we can make money, but for option, it seems that we didn't use these models to predict the future option prices? so how can we make money with these models?

Answer 1

In general there are two basic ways to make money out of your option pricing models:

Sell side (market maker, risk neutral): You use these models to calculate your greeks to hedge your portfolio, so that you live on the spread.

Buy side (market/risk taker): You use your model to find mispriced options in the market and buy/sell accordingly.

(A third possibility would be to write fancy books and papers about these models and get rich and/or tenure this way ;-)

Answer 2

Agree with all of vonjd's points though I like to add the following:

• First of all, market practitioners do not read options prices or set options prices in the market, they price the option through models primarily on the basis of implied volatility. Implied volatility is actually traded, options prices are what come out on the other side. I know there was a discussion in which some others disagreed with such a notion but just imagine you are to trade a listed index option written on the Nikkei 225 index. How do you know whether March 2013, 10500 put is correctly priced at 300 yen, 5000 yen, or 10 yen? My point is you don't know until you make implied volatility your starting point. You know that Nikkei 225 2-3 month implied vols certainly do not trade at 50 right now, not 30, but more like in the 12-20 range. You form an opinion where the implied vol should specifically lie and then price the option using a translation tool such as B-S. That is how most market practitioners trade options.

So you need to strictly differentiate between volatility modeling tools and on the other side option pricing models. Each model is more applicable to certain asset classes than others which is why you have different models in the first place. Also, you may have a different opinion on how implied vols drive the option price or form certain opinions about other dynamics and thus chose a model that fits your mindset or alter certain models and customize one to fit your style.

How do you make money with such models? Well as I said you need to make sure you delineate volatility forecasting and modeling tools from pricing tools. If you are better at forecasting volatility than others then you have a clear edge in this market.

But at the same time it can also happen that different pricing tools make the difference between someone making 20-50 million USD a year and someone who barely breaks even: Because of the nonlinearity of derivatives (but also because of other factors), different models do give you different prices even you plug in the same implied volatility. Its harder to make a difference in plain vanilla products but it can make a huge difference when you price exotic derivatives. Such exotics are places where it really shows whether a trader and quant group truly understands how to model and calculate the standard greeks and higher order moments.

You need to start with the basic tenet that what you see on the screen is not an efficient market, thus there are times when the prices you see are away from fair value because a) people use imperfect models to translate vols -> prices, and b) because people input poorly determined implied vols into their machines. That is what makes the difference between someone making and the other losing money

Answer 3

Not all stocks make for profitable options trades, even when they have options, so my first and foremost use of BSM is to screen the hundreds of optionable stocks based on their prices and some other assumed values like volatility (say 30%, above which things get expensive), dividend yield (simply 0, or 1/1200, or some other arbitrary numbers), and interest rate (readily available on sites like Pre-market CNN, and fairly stable over months). A quick calculation tells me if the option premiums are worth more than the commission and initial outlay combined and a trip online to look up a stock's Option Chain or Analysts' Ratings for more details.