### Abstract:

Derivatives are used in hedging European options against risks. The partial derivatives of
the solution with respect to either a variable or a parameter in the Black-Scholee model are
called risk parameters or simply the Greeks. Nonlinear versions of the standard Black-
Scholes Partial Differential Equation have been introduced in financial mathematics in
order to deal with illiquid markets. Market liquidity is relevant in the risk management of
derivatives since in an illiquid market the implementation of a dynamic hedging strategy
affects the price process of the underlying. Different hedging strategies and suitable
pricing adjustments are needed. We studied the Greek parameters of a nonlinear Black-
Scholes Partial Differential Equation whose nonlinearity is as a result of transaction costs
for modelling illiquid markets. The objective of this study was to compute the Greek
parameters of a European call option in illiquid markets whose illiquidity is arising from
transaction costs. This is in relation to Cetin et al. model in which transaction costs
have been incorporated (with zero interest rate). These Greeks were compared with those
derived from the formula of Bakstein and Howison (2003) equation (with positive interest
1
rate). All these Greeks were of the form a+ - j(S, t). The methodology involved deriving
p
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. Greeks show how to protect one's position against
adverse movements in critical market variables such as the stock price, time and interest
rate.