How Option Pricing Models Support Market Making, Hedging, and Risk Management

# How are Option Pricing Models used in Industry/Practice?


# How are Option Pricing Models used in Industry/Practice?












I am an MSc Financial Mathematics student, and I am struggling to grasp how stochastic models (e.g., Heston, SABR, etc) are applied in real-world scenarios. Is the following correct?

Say I am a market maker for options, my approach would involve selecting a model (e.g., Merton jump diffusion) to price options on (for example) the S&P500. At the beginning of each trading day, I would observe options market quotes (my first confusion arises here: are these quotes influenced by supply and demand? Are they provided by other market makers?) and calibrate my model (i.e., estimate model parameters) with them. Once calibrated, I determine a theoretical fair value, setting bid prices below and ask prices above this value to profit from the bid-ask spread.

The fair value derived from my model indicates the cost to replicate the options' payoffs at any time and the sensitivity (the "Greeks") of my model to changes in model parameters. This enables me to hedge my position (e.g., by purchasing futures) immediately after selling or buying an option, effectively "removing" risk and profiting from the bid-ask spread.

I understand that these models also serve various other purposes, such as risk assessment and pricing exotic options. Additionally, why is speed crucial in certain scenarios, like pricing OTC exotic options? Would clients not be willing to wait a few minutes for a quote?

Thank you!

## Answer by AKdemy (score 5)

https://quant.stackexchange.com/a/81926

Listed S&P500 options are European style exercise, see CBOE. Therefore, traditional closed form Black Scholes Merton is generally sufficient.

As always, the devil is in the details, as this Bloomberg OVME example shows. You need to correctly handle things like daycount, dates (pricing date, expiry date, premium date, delivery date, time to expiry, time to delivery). Bloomberg OVML vs Quantlib shows that this is not something all professional tools do equally well.

Generally, supply and demand is the basic price finding mechanisms for anything that is sold in markets, including oranges, haircuts and derivatives. Many factors influence demand and supply though.

Vol surfaces are fundamental to market making. They also ensure no arbitrage holds and account for many shortcomings in Black Scholes (no single vol, skew, kurtosis), as demonstrated here.

OTC markets frequently quote in implied volatility directly:

- rates and

- FX

Most listed equity options are American style though. Things get a bit more involved in this case. Typically, a vol surface is built from listed prices with techniques similar to the one outlined in American option vol surface.

Greeks are, among other things needed for hedging. As sich, sensible values are important. For examples BSM theta can exceed actual market value of an option if the time to expiry is short, as shown here. Therefore, finite difference (FD) theta is frequently computed as a true 1 (working) day bump and reprice theta (shifting the valuation date one day forward and repricing).

Speed matters because you don't just have one client. You also have a book of existing deals that need to be priced and managed. If one deal would take a few minutes to price, how do you handle a book of several thousand derivatives? For instance, you can trade about 1,000,000 listed options on 1,500 underlying stocks on the Saxo Bank trading platform.