WOLFRAM|DEMONSTRATIONS PROJECT

Barrier Option Pricing within the Black-Scholes Model

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barrier type
up and out
up and in
down and out
down and in
option type
call
put
plot variable
spot
volatility
volatility
0.3
spot
100
barrier
120
time to expiry
1.
show vanilla
up and out call: price vs. spot
barrier option
strike
vanilla option
barrier
Barrier options are a particular type of exotic option in which a certain "barrier" level is specified, and then the option either "knocks in" (becomes exercisable) or "knocks out" (becomes worthless) if the underlying asset price crosses this level from above (for "down" types) or below (for "up" types). There are four types of barriers, varying according to how the barrier affects the price: "up and in", "up and out", "down and in", and "down and out". Additionally, as with regular vanilla options, barrier options come in "call" and "put" form. This Demonstration illustrates the pricing formulas for these options within the Black–Scholes framework.