A theoretical approach to volatility surfaces in the Colombian market using the jump-diffusion model

Option markets recognize that the Black & Scholes model does not account for the empirical behavior of prices. The volatility surface is the main result of such shortcoming and provides market practitioners with useful information regarding the underlying’s volatility. Colombia’s option market is almost inexistent and no volatility surface can be observed or calculated. In an attempt to lay down theoretical foundations for the local market, this paper approaches the volatility surface based on the jump-diffusion model. Results are not only intuitive and supported by developed market’s evidence, but useful for immature options markets’ development and for risk management. Tomado del resumen de esta publicación1.Introduction. Pág.1 2.Black & Scholes (B&S) model and Brownian motion. Pág.2 3.The volatility surface. Pág.9 4.Volatility surface modeling. Pág.13 5.A volatility surface model for the Colombian market. Pág.14 6.Final remarks. Pág.18 References. Pág.1