# 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
1answer
5k views

### Barrier option (autocallable) Vega profile

I have a question about the Vega profile(graph) on an autocallable option. Generally for a regular option, the vega graph looks like a normal (kinda normal) distribution with the vega highest at-the-...
1answer
221 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, ...
1answer
269 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 $L<x_0<U$ ?
1answer
638 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 ...
1answer
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 ...
1answer
248 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 ...
2answers
299 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 $\sigma^{(1)}$ (...
0answers
77 views

### Continuous option pricing: Brownian Bridge

I have a question on the proof of the formula of Sup(S) between 2 simulation points. Do you know how the prove the following formula? Thanks
0answers
103 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 ...
0answers
154 views

1answer
124 views

### How to price a barrier using monte carlo when return distribution is not iid?

this question is actually related to set the stop loss and stop return. Say after a liquidity shock, I want to place two stops, one being stop loss and another being stop return. If I use, say 10 ...
1answer
523 views

### Barrier Shifts - necessary for up-and-out call / down-and-in put?

Recently I came across the topic of barrier shift for barrier/digital options. I found that most examples centred around down-and-in puts / up-and-in call / digitals. I am wondering if we need ...
1answer
64 views

### What is the probability of two independent OU processes being above barriers at the same time?

I have two OU processes. I'd like to know the probability that during a time period 0 to T that they are both above a barrier simultaneously at least once.
0answers
64 views

### How to price a down-and-out leveraged barrier call option using Brownian motion?

I am trying to price a type of leveraged down-and-out (LDAO) barrier call option, using geometric Brownian motion. My python script is below. I am not sure how to correctly model the increasing ...
0answers
96 views

### Black-Scholes delta of a barrier (knock-out or knock-in) option

I'm trying to calculate the Black-Scholes delta of a barrier option given the following information: Whether it is knock-out or knock-in Barrier price Strike price, $X$ Current stock price, $S$ ...
0answers
29 views

### Pricing barrier option under Levy process: Biased estimate?

I want to price a down and out call, barrier option, with the underlying asset following a Levy process. I am interest on the Kou double exponential model or the NIG process, to capture asymmetric ...
0answers
398 views

### Pricing Knock Out Barrier Options by solving Black Scholes PDE (MATLAB)

This question is based on MATLAB functions. Suppose there is a stock S following the process $dS_t=(r-q)S_tdt+\sigma(S_t,t)dW_t$ r - risk-free rate, q - dividend yield, W - Weiner process The ...
0answers
106 views

### Pricing an exotic with barrier at discrete times

How would you price the following option on underlying $S$ without dividends? Time to maturity of option $\tau = 12$ months Option has a strike $K > 0$ and constant barrier $B > 0$. $t_0$ is ...