call_price_linear: Calculate modified european call option

In mociepa/ShortfallRiskHedging: Shortfall Risk Hedging for european option

Calculate modified european call option

Description

The call_price_linear function takes parameters from Black-Scholes model and returns a price of modified european call option.

Usage

call_price_linear(asset, strike, rate, vol, drift, time, End_Time, L)

Arguments

asset	a numeric vector of asset prices.
strike	numeric value, strike price for call or put option.
rate	numeric value, risk free rate in the model, r >= 0.
vol	numeric value, volatility of the model, vol > 0.
drift	numeric value, drift of the model.
time	a numeric vector of actual time, time > 0.
End_Time	end time of the option, End_time >= time.
L	a numeric value, determines where option payoff is zero, see details, L > 0.

Details

Payoff of this modified call option is:

1(asset > L)(asset - strike)^+ , when drift > rate .

1(asset < L)(asset - strike)^+ , when drift < rate .

L(asset - strike)^+ , when drift == rate , of course in this case L <= 1.

Value

A numeric vector, price of the modification of european call option using linear loss function.

Examples

call_price_linear(100, 100, 0, 0.5, 0.05, 0, 1, 120)
call_price_linear(c(100, 120), 100, 0, 0.3, 0.05, 0, 1, 120)
call_price_linear(c(100, 120), 100, 0, 0.3, 0.05, c(0, 0.5), 1, 120)

mociepa/ShortfallRiskHedging documentation built on Sept. 30, 2022, 6:43 p.m.