Friday, December 27, 2013

math tools used in option pricing vs risk mgmt - my take

In general, I feel statistics, as applied math, is a more widely used branch of math than probability. Both are used in finance. I feel their usage is different in the field of option pricing vs risk mgmt. Both efforts attempt to estimate the future movements of underlier prices. Both rely on complicated probability and statistics theories. Both try to estimate the "histogram" of a portfolio's market value on a future date.

In option pricing, the future movement of the Underlyer is precisely modeled as a GBM (geometric Brownian motion). IMHO Stochastic is probability, not stats, and is used in option math. When I google "stochastic", "volatility" always shows up. "Rocket science" in finance is usually about implied volatility -- more probability less statistics.

In VaR, future is extrapolation from history. Risk manager doesn't trust theoretical calculations but relies more on historical data. "Statistical risk management" clearly shows the use of statistics in risk management.

See other posts on probability vs stats. Risk management uses more stats than Option pricing.

Incidentally, If a portfolio include options,  then VaR would need both theoretical probability and statistics....

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