# Questions tagged [barrier]

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### How to hedge a perpetual barrier option?

I have encountered the following question during my interview: How to have a static hedging of a perpetual barrier up-and-out call option in practice? Strike K = 110, barrier B = 120 for example? MY
203 views

### Pricing 'Down and In' claims

I came across this question in a sheet of practice problems which has me a bit stumped. A down-and-out call option with maturity T, strike K = 100 and barrier L = K coinciding with the strike, ...
252 views

### What is the probability that a OU process hits an upper barrier U before a lower barrier L?

What is the probability that the arithmetic OU process $dx_t= \theta(\mu-x_t)dt+\sigma dW_t$ hits barrier $U$ before hitting barrier $L$ when $L<x_0<U$ ?
504 views

### Price of a double barrier option

Suppose an option is defined as follows. There is an upper barrier at $H$ and a lower barrier at $0$. If the stock price touches the upper barrier you get a payoff of $1$ and the trade terminates ...
2k views

### How to hedge a barrier option with vanilla options?

I want to hedge a barrier option, say a knock-out call with strike K and barrier B out-of-the-money. My idea was to start from the payoff diagram of this option, and try to accomodate it with vanilla ...
222 views

### How to price up-out-call by solving heat equation like down-out-call

We know that by changing the variables we can obtain the Black-Scholes formula of vanilla call through solving the ...
269 views

### What is the effect of mean-reversion on an upper barrier knock-out call option?

Consider a mean-reverting normal model for an underlying $dX^{(1)}_t=-\kappa X^{(1)}_tdt+\sigma^{(1)} dW^{(1)}_t$, for fixed time-independent constants, $\kappa$ (mean-reversion) and $\sigma^{(1)}$ (...
82 views

### Two barrier options puzzle

I come across an interesting question about barrier option as shown below. Two barrier options are given with the same parameters including the barrier level. The first one is knocked out when it ...