Questions tagged [barrier]

The tag has no usage guidance.

Filter by
Sorted by
Tagged with
0
votes
0answers
44 views

How to price barrier options under Black-Scholes?

I am looking for a rigorous proof for the closed form of the price of a barrier option (up-in/up-out) under Black-Scholes model, that is a step by step solution of the solution of the heat equation ...
0
votes
0answers
22 views

Pricing of a compo with barrier

i am given this exercise where i have to price a compo put option with barrier. For hypotesis the option is an Up In Put, with domestic strike $K^d$, written over a generic foreign stock $S^f=r_t^fdt+...
0
votes
0answers
39 views

Pricing barrier options with Monte Carlo Simulations

Hey I try to compute barrier option price by Monte Carlo Simulations. It's my code: ...
4
votes
0answers
69 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
1
vote
0answers
71 views

Payoff of barrier options

I was reading a research paper recently and the author defined payoffs of Up-and-Out and Down-and-Out barrier call options as max[0, ST - K]I(m < H) and max[0, ST - K]I(M > H) respectively. K is ...
1
vote
1answer
41 views

Is the moneyness of a barrier option based on the strike value or the barrier when mapping to a volatility surface?

Say you have a down and in put barrier option with a strike of 100 and barrier at 60. If the stock price sits at 90, which value would you use to determine the moneyness? Is the option in or out of ...
0
votes
1answer
51 views

Issue in Pricing Barrier Options using MCBarrierEngine in QuantLib Python

Extremely sorry for bugging the community again, but I am struggling with finding proper documentation of QuantLib Python. I am trying to price Barrier Option using MC Simulation. Here is the code: <...
0
votes
0answers
93 views

COS method option pricing

is the cos method used to calculate prices of options other than the European call? Or is this method only used for calibration? Is it possible to evaluate the barrier and lookback options? I am ...
0
votes
0answers
38 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 <...
1
vote
2answers
79 views

Graph of a down-and-in barrier option

Here is a graph of Price vs Spot from Joshi's Quant Interviews book, The first line is a down-and-out barrier option and the other one is a down-and-in barrier option. The strike is 100 and the ...
1
vote
0answers
59 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 ...
0
votes
0answers
50 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.. ...
1
vote
1answer
63 views

Sample path simulation using two random variables

I was wondering if there is a way of generating a sample path of a Geometric Brownian Motion using two independent standard normal random variables instead of just one. The exact scheme that uses ...
0
votes
0answers
21 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 ...
0
votes
0answers
31 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 $...
1
vote
1answer
114 views

Valuation Down-And-Out Put Option via Rubinstein Closed-Form Solution

I am trying to understand the closed form solution for evaluating a down-and-out put option of Rubinstein and Reiner (1991) as stated in Baule and Tallau (2011) for the valuation of bonus certificates....
1
vote
2answers
94 views

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 ...
0
votes
1answer
114 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 ...
3
votes
1answer
141 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 ...
3
votes
0answers
112 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.
1
vote
0answers
64 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, $S$ ...
1
vote
1answer
92 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 ...
1
vote
1answer
55 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&...
1
vote
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 ...
0
votes
1answer
136 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 ...
0
votes
0answers
978 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 ...
1
vote
0answers
306 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 ...
1
vote
0answers
91 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 ...
4
votes
0answers
92 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 ...
8
votes
3answers
356 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
4
votes
0answers
147 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 ...
3
votes
1answer
145 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 ...
1
vote
1answer
121 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 ...
1
vote
1answer
444 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 ...
1
vote
1answer
1k 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?
3
votes
1answer
214 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 ...
1
vote
0answers
327 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.
1
vote
0answers
720 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 $$C_T := \max(S_T-K,0)1_{M_T \geq L}$$ ...
2
votes
0answers
130 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? ...
1
vote
1answer
63 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.
1
vote
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 ...
1
vote
2answers
267 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 ...
0
votes
1answer
445 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 ...
5
votes
1answer
212 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, ...
2
votes
1answer
127 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 ...
4
votes
1answer
4k 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-...
2
votes
2answers
11k 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 (...
1
vote
1answer
422 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
votes
1answer
501 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 ...
2
votes
0answers
850 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)...