Questions tagged [barrier]

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Deltas on Barrier options vs Vanilla options

In "Heard on the Street" it states that $$\Delta_{\text{up and out call}} \leq \Delta_{\text{standard call}} \leq \Delta_{\text{down and out call}}$$ Is there an intuitive explanation for why this ...
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1answer
78 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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1answer
54 views

Price Down and In Barrier Option Using Local Vol and Monte Carlo

As an entry level financial engineer, I'm trying to make sense of a practical case using the concepts I learned including local vol, monte carlo, so I really appreciate your advice if my understanding ...
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0answers
62 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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0answers
38 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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1answer
62 views

Hindsight overhedge for pricing path dependent options

I understand how to use the longstaff schwartz method in Monte Carlo to compute the continuation value of path dependent options but someone recently mentioned another technique called "Hindsight ...
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1answer
45 views

In search of double barrier out option on a BM

We have a BM $X_t$ with $dX_t=\sigma dB_t$ ($X_0$ not necessarily zero!) under the risk neutral measure $\Bbb Q$. Given upper barrier $U$, lower barrier $L$, "strike" $K$ such that $L<X_0<U, L&...
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0answers
20 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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1answer
87 views

Barrier option on a basket with arbitrary stochastic process

Suppose I want to price a Down-and-out European call, barrier option. However, the stochastic process is not a gBm or any other Levy process with known structure. Practically, I want a barrier option ...
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0answers
28 views

Crank–Nicolson for Discrete Type Barrier: Backward propagation

The boundary conditions for Discrete Type Barrier (e.g. Up-and-Out) are: - Dirichelet boundary condition (set to 0 when spot is bigger than Barrier) on Barrier event dates - Otherwise (the other sides ...
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0answers
64 views

European Knock-Out Option with European Barrier

I have two problems: 1) Actually i didn't find anywhere a precise definition of European Knock-Out Option with European Barrier. 2) Assuming that European means that it depends only on starting ...
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0answers
193 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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0answers
167 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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0answers
68 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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0answers
67 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 ...
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3answers
256 views

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
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0answers
120 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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1answer
106 views

Fair value of a binary cash-or-nothing option with a barrier

I want to find the fair value of a European cash-or-nothing option that pays \$1 if $S_t>K$ and $S$ breached the level $M<0<K$, where $S$ is the risk-neutral process $dS_t=\sigma dW_t$. My ...
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1answer
101 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 ...
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0answers
279 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 ...
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1answer
667 views

how to price barrier option under local vol model using QuantLib

I use QuantLib in Python. Now I have implied volatility surface data. How can I get the local vol surface than using finite difference method to price a barrier option in QuantLib?
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1answer
164 views

Barrier Option under Jump Diffusion

I am trying to price a Barrier Option under a model with jumps. I am using a brownian bridge approach but struggle with the jumps around these bridges and don't know how to handle this. My main ...
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0answers
237 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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0answers
501 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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0answers
113 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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1answer
62 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.
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1answer
2k views

Pricing a double barrier option using Monte Carlo (C++ & Python code included)

I'm trying to price an option with upper and lower barriers using MC where the payoff is $B_u$ when $S_t > B_u$, $B_l$ when $S_t < B_l$ and $S_t$ when $B_l < S_t < B_u$. I have written ...
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2answers
204 views

Double knockout binary pricing?

I'm studying the pricing of a Double-Barrier binary option on the price of $S$. By this I mean an option that pays $X$ at maturity $T$ if the lower ($H1$) or upper barriers ($H2$) are not hit during ...
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1answer
320 views

Down-Out Call and Vanilla call price

We all know from text books and practice that a knock out call is usually cheaper than a vanilla call option. Economically speaking, this comes from the fact that there is a probability bigger than ...
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1answer
195 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, ...
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1answer
87 views

Pricing Secured Barrier Call 2

EDIT: OK, I understand the reasoning for the initial answer now; however, I don't understand why we would need the digital call with a strike of 33 in this question. Is it just there to serve as a red ...
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1answer
3k 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-...
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2answers
8k views

Delta hedging on Barrier/Digital Options

I would like to adress a question I have in mind and I didn't found a clear answer online. When we deal with Barrier or Digital Options we have a discontinuty in the payoff, so that the derivatives (...
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1answer
329 views

How to use reflection principle to solve the analytic solution of double barrier-out-call

We consider up/down-out-call whose payment $$V(T,S_T) = \Psi(S_T)\mathbb{II}(S_T),\ V(t,B) = 0.$$ Here the range constraint function is ...
3
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1answer
400 views

First passage probability formula

I recently read an article and they provide a formula for the first-passage probability as $$Z = {1 \over \sigma }\left[ {\log S/{S_t} + (r - {1 \over 2}{\sigma ^2})t} \right]$$ ${{S_t}}$ value of ...
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0answers
693 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)...
3
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1answer
429 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 ...
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2answers
207 views

The PDE of the probability hitting the barrier before T

Suppose: $$d S=\mu S dt+\sigma Sd W$$ $Q(t,S)$ is the probability that $S$ hit the barrier $B(S_t<B)$ before $T,$ then $Q$ satisfies following PDE $$Q_t+\dfrac{1}...
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1answer
206 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 ...
3
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1answer
144 views

Barrier Derivative Pricing

Assume constant interest rate $r$ and a stock with current price at $S_0$ that pays no dividend (assume $S_t\ge0$). When the stock price hits the barrier $B$ (where $B<S_0$) you receive \$$1$ and ...
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1answer
121 views

How to price barrier options with making in model-independent way?

I have to use simple no arbitrage arguments to find the price of a barrier option where initial stock price $S_0 = 100$ and barrier/strike $B = K = 80$. Here we don't assume geometric Brownian motion ...
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2answers
230 views

Valuation of FX vs. Commodities Barrier Options

With reference to my previous question about the computation of a barrier option delta, @LocalVolatility referenced a nice closed form solution to value barrier options on a stock paying a dividend ...
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1answer
219 views

Strange Delta for FX Down And Out Call, Strike below Barrier

Based on this text about FX options on pages 139, 141 and 145 I'm trying to compute the delta of a down and out call with the strike below the barrier. Here is a quick and dirty Python code (I assume ...
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1answer
294 views

PDE of barrier and lookback options

In Shreve's book, he obtain the PDE of barrier option by Payment function $$V(T) = (S(T) - K)^+\mathbb{II}_{\{S_{\textrm{max}}(T) > B\}}$$ Then use the risk neutral pricing formula and Markov ...
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1answer
110 views

Pricing Secured Barrier Call

A European barrier call with barrier $B = 50$, expiration $T = 31$, and strike $K = 33$ costs $12$. The investor is interested in a product that, unlike this barrier call, offers some protection for ...
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1answer
53 views

Clarification on the payoff of a portfolio consisting of a long Up&In Put and short Up&In Call

I am trying to make sense of this example: I'm not following the second line in red: "If you buy an up-and-in put and sell an up-and-in call, the payoff is the strike price minus the stock price ...
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1answer
606 views

What is the probability that a Brownian Bridge hits an upper barrier $U$ before a lower barrier $L$?

The probability that an arithmetic Brownian motion process $dt = \mu dt + \sigma dW$ hits an upper Barrier $U$ before it hits a lower barrier $L$ is given by $$ \mathbb{P}(\tau_U\leq \tau_L) = \frac{\...
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1answer
234 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 $L<x_0<U$ ?
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1answer
365 views

Probability of Brownian motion particle touching barrier given path starts at $X_0$ and ends at a known $X_t$

I have been reading Su and Rieger's paper on barriers and from there have been able to work out the unconditional probability of the process $dXt = μ dt + σ dWt$ touching a down barrier $α$ to be $\...
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1answer
72 views

Why is H always* the letter used to describe the level of a barrier?

A quick and (hopefully) easy question. Why? *(always / often / when it's not B)