Why Accurate American Option Pricing Matters for Hedging and Valuation

# Why is accuracy important in pricing American Options?


# Why is accuracy important in pricing American Options?












I see a lot of academic papers talking about accuracy in pricing American Options (and finding analytic solutions). Why is there so much interest in this topic? Isn't the option price set by the market? From what I can understand, accuracy in pricing gives accuracy in implied volatility, which gives you a sense of which options are expensive relative to others (eg. A listed puts for the same underlying, same maturity but varying strike may have different volatilities, even though they should be the same). I don't see why as an option trader accuracy is important, since the market already decided the fair price.

## Answer by jherek (score 1)

https://quant.stackexchange.com/a/73521

Accurate pricing of American options is useful in both situations, where the option is quoted (listed/exchange traded option), as well as where the option is not quoted (over the counter/OTC). Listed options are only available for specific underlyings, specific strike prices and specific maturities.

- For listed options, the accurate pricing will give you a reliable hedge for your option, typically via the delta greek. The most popular model is indeed Black-Scholes, because it is simple to understand, but there are variations, for example considering a term-structure of volatilities/rates. Slightly more fancy models such the local volatility model or stochastic volatility models are usually not used in this context.

- For OTC options, the pricing model may help you infer the price of the American option from European options prices. Yes, to quote a price, you don't necessarily need to be extra accurate (up to the cent may be enough), since you will add a spread anyway. The model also gives you a simple way to delta hedge and vega hedge your American options. Local/stochastic volatility models may offer here some interesting alternate price, which you can take into account to define your spread. Accuracy gives you some comfort that your implementation is reliable/theoretically sound. If your pricing is consistently too low under some circumstances, the counterparties may take advantage of it.

- In both cases, the greeks are often computed via numerical bump and revalue, and stress the accuracy of your implementation more.

Contrary to some of the comments, the American option price may be significantly different from its European counterpart. This typically happen when early exercise is often optimal (you are close to the early exercise boundary).

## Answer by Bernd (score 0)

https://quant.stackexchange.com/a/40355

The market creates price quotes only for some standard products. But maybe you have some products in your portfolio that are non standard (e.g. because the market has changed since you bought it).

Now you want to know what your assets are worth. What to write to your balance sheet? Or maybe you want to sell it. how much should you be payed? The market doesn't tell you directly. You have to to calculate it. And typically you want to know it exactly.