Abstract:
Derivatives are used in hedging European options against risks. The partial derivatives
of the solution to either a variable or a parameter in the Black-Scholes model are called risk
(Greek) parameters or simply the Greeks. Nonlinear versions of the standard Black-Scholes
Partial Differential Equations have been introduced in financial mathematics in order to
deal with illiquid markets. In this paper we derive the Greek parameters of a nonlinear
Black-Scholes Partial Differential Equation whose nonlinearity is as a result of transaction
costs for modeling illiquid markets. We compute the Greek parameters of a European call
option price from the nonlinear equation ut +
1
2
σ
2S
2uSS(1 + 2ρSuSS) = 0. All these Greeks
were of the form a +
1
ρ
f(S, t). The methodology involved deriving the Greek parameters
from the formula of the equation by differentiating the formula with respect to either a
variable or a parameter. These Greeks may help a trader to hedge risks in a non-ideal
market situation.
