European Option Prices and Greeks in 3D
European Option Prices and Greeks in 3D
This Demonstration displays the prices of European call options, put options, or the "Greeks" associated with these options (delta, gamma, vega, theta, and rho). The display is 3D, with the stock price on the axis and the days to expiration on the axis. Sliders let you change the strike price, risk-free rate, and volatility parameters. You can see how a specific parameter realization travels across the 3D surface as the stock price changes and time to expiration approaches.
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The 3D surface clearly shows how the call (or put) price curve changes shape and approaches the intrinsic value curve as time to expiration approaches. Alternatively, the delta parameter becomes very steep as expiration approaches, and this steepness is seen as the gamma parameter spikes for near-the-money options as expiration approaches. The vega parameter surface shows the influence of (a constant) diminishing of volatility as expiration approaches or the stock price moves away from the strike price. To further aid in understanding, you can drag to rotate the 3D displays to match the two-dimensional graphs available in most financial derivatives textbooks.