Finance_European_single-barrier_knock-in_call

This is a CRR binomial tree program that prices European single-barrier knock-in calls on a dividend-paying stock, and also determines the relative error based on the call price using the Black-Scholes model.

Notes

Let c1 be the price from the tree program and c2 be the price from the Black-Scholes model. The relative error will be 100[(c1 -c2)/c2] (%)

Inputs and outputs

For this project, we have:

1. Inputs: S (stock price), X (strike price), H (barrier, smaller than S), t (years), s (volatility in %), r (interest rate in %), q (dividend yield in %), and n (number of periods).
2. Output: Price c1 from the tree program, price c2 from the Black-Scholes model and the relative error.

Usage

In MatLab, just run the given file.

Example

1. Suppose S = 95, X = 100, H = 90, t = 1 (year), s = 25 (%), r = 15 (%), q = 5 (%), and n = 192:
   1. The price given by the tree is c1=5.3840.
   2. The price given by the Black-Scholes model is c2=5.3844.
   3. The relative error is -0.0083%.

2. Suppose S = 95, X = 100, H = 90, t = 1 (year), s = 25 (%), r = 15 (%), q = 5 (%), and n = 193:
   1. The price given by the tree is c1=4.1270.
   2. The price given by the Black-Scholes model is c2=5.3844.
   3. The relative error is -23.3527%.