Chapter 19FX Derivatives Pricing Models

FX derivatives trading desks use pricing models to value exotic contracts. Pricing models extend the Black-Scholes framework by adding new elements into the model dynamics. Different pricing models have different spot, volatility, and interest rate dynamics, which in turn generates different prices on exotic contracts. When using any pricing model it is vital to understand the model dynamic and how this dynamic impacts pricing.

Exhibit 19.1 shows the high-level connections between vanilla options, exotic options, probability density functions, and exotic pricing models.

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Exhibit 19.1 FX derivatives valuation framework

Exotic pricing models are split into two main categories:

  1. Smile models incorporate the volatility surface. All smile models are calibrated to the volatility surface, plus some smile models have additional calibration to exotic contracts. Common smile models are stochastic volatility, local volatility, mixed volatility, and jump diffusion. Smile models often have static or deterministic interest rates.
  2. Interest rate models incorporate stochastic (i.e., randomly moving) interest rates in order to correctly value the effects of interest rate volatility and spot versus interest rate correlation. These effects are particularly important on long-dated contracts. Interest rate models often have static or deterministic volatility ...

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