Option Calibration & Pricing

While theoretical valuation model provides a model to evaluate the value of a given derivative, the market-based model tries to fit the model that can replicates the observed prices of a derivative. It is called option calibration. 

Once a derivative is calibrated, we can proceed to evaluating, trading, investing, hedging and de-risking stocks and options portfolio.   

Market
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We have to consider various market risks in order to valuate a derivative:

  • Price Risk
  • Volatility Risk
  • Jump or Crash Risk
  • Interest Rate Risk
  • Correlation Risk
  • Liquidity Risk
Theoretical Valuation
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Black-Scholes-Merton (BSM) model

Cox-Ross-Rubinstein (CRR) model

Fourier-based model

American option valuation via 

  • Binomial Trees
  • Monte-Carlo Simulation
Market-based Valuation
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Merton’s jump-diffusion model

Bakshi-Cao-Chen (BCC) model

Cox-Ingersoll-Ross (CIR) model