Questions tagged [barrier]
The barrier tag has no usage guidance.
26
questions with no upvoted or accepted answers
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0answers
188 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)...
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
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 ...
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:
$$dS_t=\mu S_tdt+\sqrt{v_t}S_tdW^S_t$$
$$dv_t=\kappa(\bar{v}-v_t)dt+\eta\sqrt{v_t}dW^v_t,\quad d\langle ...
3
votes
0answers
112 views
How are Autocallables modelled?
What models are used to price autocallables ? Should we talk about Heston/SABR models which talking about this topic ? Any reference link is welcome.
3
votes
0answers
76 views
Range options in BS
I know how barrier options are priced in Black-Scholes scheme.
I'm wondering if an analytical formula exists also for range (corridor) digital options i.e. options paying only if the price remains ...
3
votes
0answers
895 views
Law of a geometric brownian motion first hitting time (formula dont match Monte Carlo Simulation)
I posted this question before on MSE
I need to use it in a small step in the middle of a simulation and
I think I'm not getting correct results to this probabilities and so
for my all ...
2
votes
0answers
130 views
Barrier Option with Time-Dependent Rebate
Is there a closed form solution for American Single-Barrier Options (specifically Down-and-Out Calls) which undergo linear principal amortization based on the amount of time passed before being KO'ed?
...
2
votes
0answers
850 views
Greeks(theta) of a Down-and-Out barrier option
I am trying to figure out the theta for a down-and-out barrier put option. After some research of my own, I found out that a down-and-out put can be expressed as
$$
P_V(S_0, S_0)-P_V(S_0, H)-(S_0 - H)...
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
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 ...
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
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 ...
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 ...
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
$$C_T := \max(S_T-K,0)1_{M_T \geq L}$$
...
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
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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:
...
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
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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 <...
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..
...
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 $...
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 ...
