EuropeanCall: Computing Prices of European Calls with a Binomial Tree

In NMOF: Numerical Methods and Optimization in Finance

Description

Computes the fair value of a European Call with the binomial tree of Cox, Ross and Rubinstein.

Usage

EuropeanCall(S0, X, r, tau, sigma, M = 101)
EuropeanCallBE(S0, X, r, tau, sigma, M = 101)

Arguments

S0	current stock price
X	strike price
r	risk-free rate
tau	time to maturity
sigma	volatility
M	number of time steps

Details

Prices a European Call with the tree approach of Cox, Ross, Rubinstein.

The algorithm in EuropeanCallBE does not construct and traverse a tree, but computes the terminal prices via a binomial expansion (see Higham, 2002, and Chapter 5 in Gilli/Maringer/Schumann, 2011).

Value

Returns the value of the call (numeric).

Author(s)

Enrico Schumann

References

Gilli, M., Maringer, D. and Schumann, E. (2011) Numerical Methods and Optimization in Finance. Elsevier. http://www.elsevierdirect.com/product.jsp?isbn=9780123756626

M. Gilli and Schumann, E. (2009) Implementing Binomial Trees. COMISEF Working Paper Series No. 008. http://comisef.eu/?q=working_papers

Higham, D. (2002) Nine Ways to Implement the Binomial Method for Option Valuation in MATLAB. SIAM Review, 44(4), pp. 661–677. http://personal.strath.ac.uk/d.j.higham/papers/binom.pdf .

See Also

callHestoncf

Examples

## price
EuropeanCall(  S0 = 100, X = 100, r = 0.02, tau = 1, sigma = 0.20, M = 50)
EuropeanCallBE(S0 = 100, X = 100, r = 0.02, tau = 1, sigma = 0.20, M = 50)

## a Greek: delta
h <- 1e-8
C1 <- EuropeanCall(S0 = 100 + h, X = 100, r = 0.02, tau = 1,
                   sigma = 0.20, M = 50)
C2 <- EuropeanCall(S0 = 100    , X = 100, r = 0.02, tau = 1,
                   sigma = 0.20, M = 50)
(C1 - C2) / h

Example output

[1] 8.876513
[1] 8.876513
[1] 0.6338935

NMOF documentation built on May 2, 2019, 6:39 p.m.