Kou’s Model is a stochastic process used in quantitative finance for option pricing, specifically designed to account for asset price movements that exhibit both continuous diffusion and sudden, unpredictable jumps. In crypto option pricing, its purpose is to provide a more realistic valuation framework than models like Black-Scholes, which assume continuous price paths, by incorporating the frequent and significant price jumps characteristic of highly volatile digital asset markets.
Mechanism
The model extends the standard Black-Scholes framework by adding a jump component, typically modeled as a compound Poisson process with double exponential jump sizes. This mechanism allows for distinct probabilities of upward and downward jumps of varying magnitudes, which are superimposed on a continuous geometric Brownian motion. Parameters include jump intensity, mean jump size, and volatility of jump sizes.
Methodology
Applying Kou’s Model involves calibrating its parameters to historical crypto market data, particularly the observed frequency and magnitude of price shocks. This calibration often utilizes maximum likelihood estimation or other statistical techniques to fit the model to option prices or underlying asset returns. The methodology enhances risk assessment and pricing accuracy for institutional crypto options, offering a more nuanced understanding of tail risk and extreme market events.
Calibrating jump-diffusion models for crypto options is a complex task due to the ill-posed nature of the problem and the unique statistical properties of the underlying assets.
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