Questions tagged [barrier]

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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 ...
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141 views

Zero-rebate barrier option pricing under the Heston model

I'm trying to derive an approximation for the zero-rebate barrier option under the Heston model: $$dS_t=\mu S_tdt+\sqrt{v_t}S_tdW^S_t$$ $$dv_t=\kappa(\bar{v}-v_t)dt+\eta\sqrt{v_t}dW^v_t,\quad d\langle ...
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187 views

Simple way to get the crossing probabilities of a moving barrier

Hello Quant Finance StackExchange, Is there a simple way to find the crossing probabilities of a moving barrier, namely a barrier written in the form $U(t)=\alpha_1t^2 + \beta_1t + \gamma_1$ and $L(t)...
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90 views

How are Autocallables modelled?

What models are used to price autocallables ? Should we talk about Heston/SABR models which talking about this topic ? Any reference link is welcome.
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76 views

Range options in BS

I know how barrier options are priced in Black-Scholes scheme. I'm wondering if an analytical formula exists also for range (corridor) digital options i.e. options paying only if the price remains ...
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872 views

Law of a geometric brownian motion first hitting time (formula dont match Monte Carlo Simulation)

I posted this question before on MSE I need to use it in a small step in the middle of a simulation and I think I'm not getting correct results to this probabilities and so for my all ...
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120 views

Barrier Option with Time-Dependent Rebate

Is there a closed form solution for American Single-Barrier Options (specifically Down-and-Out Calls) which undergo linear principal amortization based on the amount of time passed before being KO'ed? ...
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796 views

Greeks(theta) of a Down-and-Out barrier option

I am trying to figure out the theta for a down-and-out barrier put option. After some research of my own, I found out that a down-and-out put can be expressed as $$ P_V(S_0, S_0)-P_V(S_0, H)-(S_0 - H)...
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45 views

Do barrier options have closed form values for Greeks?

This may be quite simple but I was wondering if barrier options, and more particularly up-and-out European call options have closed form values for the Greeks?
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56 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 ...
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48 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, $S$ ...
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27 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 ...
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239 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 ...
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84 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 ...
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283 views

What is the vega profile of an up-and-out call option? And why is this important in structuring?

I had this question during an interview but I can't seem to find the answer on the internet.
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669 views

Black-Scholes equation for barrier options

I would like to write down the PDE for the price of an up-and-in call option under the Black-Scholes model as follows. The payoff of the option at expiry $T$ is $$C_T := \max(S_T-K,0)1_{M_T \geq L}$$ ...
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28 views

How to calculate Greeks for leveraged Barrier options?

I am wondering how to calculate option Greeks for Down-and-out barrier Call options with leverage. The option characteristics are as follows. The buyer of the option pays a fraction of the spot price <...
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35 views

Barrier option with zero-strike

Good morning, everybody, I would like to know whether an up-and-out call option with a zero strike has a special name in the list of exotic options or is still a special case of a barrier option.. ...
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15 views

Static hedge for Down-and-out put option

I am trying to compute the static hedge for a down-and-out put option with the barrier above the strike using the put-call symmetry. I am okay with the example in the note with the call option but I ...
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25 views

Initial price of digital option with barrier

Given that $S_0 = 1, u = \frac{5}{4}, d = \frac{4}{5}, r = \frac{1}{40}$: The payoff of a digital option with a barrier B > S_0 on the running maximum is: 1 if $max\{S_0, ..., S_n\} \geq B$ 0 if $...
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1answer
93 views

What is the go-to method for numerical pricing of discrete barriers?

There are tons of methods for pricing discrete barrier options in various models? What is the go-to "classical" method that is most popular? Hopefully not Monte Carlo (significant accuracy would ...
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586 views

What exactly does shifting a barrier in a barrier option mean and how does it hedge delta?

How exactly is shifting the barrier to hedge delta implemented in case of barrier options. Is it just changing the barrier, if so, how does it hedge delta or is it making the barrier a range like a ...
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1answer
112 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 ...