Questions tagged [barrier]
The barrier tag has no usage guidance.
19
questions with no upvoted or accepted answers
4
votes
0answers
118 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 ...
4
votes
0answers
181 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)...
3
votes
0answers
62 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 ...
3
votes
0answers
74 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
840 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
108 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
0answers
30 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
136 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
67 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
261 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
130 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
225 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
423 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}$$
...
1
vote
0answers
654 views
Greeks(theta) of a Down-and-Out barrier option
I am trying to figure out the theta for a down-and-out barrier put option. After some research of my own, I found out that a down-and-out put can be expressed as
$$
P_V(S_0, S_0)-P_V(S_0, H)-(S_0 - H)...
0
votes
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 ...
0
votes
0answers
25 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 ...
0
votes
0answers
59 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 ...
0
votes
0answers
124 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 ...
0
votes
1answer
85 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 ...
