WOLFRAM|DEMONSTRATIONS PROJECT

Adaptive Mesh Trinomial Tree for Vanilla Option Pricing

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underlying,
S
0
49.63
strike, K
55
volatility, σ
0.592
risk-free rate,
r
f
0.01
dividend yield, q
0.0607
days to maturity, T
90
number of steps, N
8
option type
Put
Call
exercise style
European
American
mesh steps
2
Initialization timed out

This Demonstration illustrates the application of the recombining adaptive mesh trinomial tree method to numerically approximate the value of the European- or American-type vanilla call/put option, assuming constant volatility and risk-free rate. The adaptive mesh trinomial tree method reduces nonlinearity error and improves pricing efficiency (e.g., reduces CPU time) by overlaying a higher-resolution mesh tree over the conventional coarse tree lattice [1]. The method may be used to approximate the implied volatility parameter for European- or American-type vanilla call/put options. Furthermore, the trinomial adaptive mesh tree method may be extended to estimate the value of other types of options (e.g., barrier options).
Hover over each tree node to view the price of the underlying security (top) and value of the option (bottom) displayed in the tooltip. Optimal option exercise is indicated by red circles for relevant tree nodes. In the case of the European-type call/put options, the optimal exercise refers to instances when the European call/put option is in the money at expiration—the underlying asset price is greater than the strike price. In the case of American-type call/put options, the optimal exercise refers to instances when the American-type call/put option is in the money at expiration as well as when the value of immediate exercise (the underlying asset price minus the strike price) before expiration is greater than the value of continuing with the option. Further, instances when the immediate exercise value is greater than the value of continuing with the option also constitute the optimal exercise price of the American-type call/put option.