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September 1st, 2016, 1:39 pm
Forum: Student Forum
Topic: Compatibility condition
Replies: 3
Views: 654

### Re: Compatibility condition

ok, so what you are saying the function is smooth, meaning I have all kinds of partial derivatives, however, it is magnitude is very large(think 1/x as s approaches 0). And numerically it is hard to capture this type of functions?
August 29th, 2016, 7:08 pm
Forum: Student Forum
Topic: Compatibility condition
Replies: 3
Views: 654

### Compatibility condition

For the barrier option we often have 0 on the boundary and likely some positive payoff on the right of the boundary. So the data is not compatible. Why is this a problem? the solution for any t<T is infinitely smooth as it can be shown mathematically deriving the exact solution, so why do I care ab...
August 29th, 2016, 5:39 pm
Forum: Student Forum
Topic: Fichera for transport equation
Replies: 1
Views: 325

### Fichera for transport equation

Hi, I think I understood how to apply Fichera criteria to the Black Scholes type of equation and I see it is mentioned it was originally developed for elliptic type of equations. We can consider BS eq as elliptic such that it degenerates for all t and therefore we need terminal condition for t=T. Ho...
August 10th, 2016, 8:11 pm
Forum: Student Forum
Topic: American call on a dividend paying stock
Replies: 11
Views: 1034

### Re: American call on a dividend paying stock

The modification of your algorithm for calls to make it work for puts is pretty simple.  (I  assume $r > 0$ and no other carry costs besides the discrete dividends). For calls, it suffices to check for early exercise at $t = t_D-$, instantaneously prior to the ex-date. For puts, you need to...
August 10th, 2016, 5:19 pm
Forum: Student Forum
Topic: American call on a dividend paying stock
Replies: 11
Views: 1034

### Re: American call on a dividend paying stock

I don't own the book so I can't just lookup that chapter. I referred to the paper because this is something accessible to everyone as of today. And I still did not get my answer, just shown the results. At least from the paper I could see from formula 5 how the model is implemented for calls. All I ...
August 9th, 2016, 7:06 pm
Forum: Student Forum
Topic: American call on a dividend paying stock
Replies: 11
Views: 1034

### Re: American call on a dividend paying stock

early exercise decisions always get back to "what do i give up" versus "what do i get" - in the case of a put, ask yourself in the current interest rate environment what you get
I am using a numerical algorithm to solve this problem and it has to work in any environment.
August 9th, 2016, 7:05 pm
Forum: Student Forum
Topic: American call on a dividend paying stock
Replies: 11
Views: 1034

### Re: American call on a dividend paying stock

One approach is this
http://www.nccr-finrisk.uzh.ch/media/pdf/ODD.pdf

and the update in Alan's new book (chapter 9 AFAIR).
Alan,
can you please comment on puts? In the paper, only calls are considered in details. Puts are only mentioned.
August 4th, 2016, 7:27 pm
Forum: Student Forum
Topic: American call on a dividend paying stock
Replies: 11
Views: 1034

### Re: American call on a dividend paying stock

One approach is this http://www.nccr-finrisk.uzh.ch/media/pdf/ODD.pdf and the update in Alan's new book (chapter 9 AFAIR). ok, I looked through the paper and it confirms that my scheme is correct. However, it only considers the call option in details. And clearly If I want to exercise, I better do ...
August 4th, 2016, 1:50 pm
Forum: Student Forum
Topic: American call on a dividend paying stock
Replies: 11
Views: 1034

### American call on a dividend paying stock

I would like to show that American call can be exercised early if the stock pays dividend. So, I have a code to value an American call, what I need to know is how to incorporate the dividend. Most FDM books say dividends are set through V(t+,S)=V(t-,S-d), so basically if I implement it, I do: 1. Ass...
August 4th, 2016, 1:37 pm
Forum: Student Forum
Topic: Exercise boundaries for american call and put
Replies: 21
Views: 1475

### Re: Exercise boundaries for american call and put

It sounds like you may indeed be able to leave the exercise boundary as an internal matter for your solver and not include it in your output (which is the typical design). There are two practical use cases (that I can think of off the top of my head) where you may want access to the boundary. The f...
August 4th, 2016, 12:35 pm
Forum: Student Forum
Topic: Exercise boundaries for american call and put
Replies: 21
Views: 1475

### Re: Exercise boundaries for american call and put

There are a couple of different ways to think about this. The general approach is applicable in a world of stochastic rates and volatility, you just have to parameterize their processes and solve the optimal stopping time problem in a richer space, and my comment remains correct, mutatis mutandis. ...
August 3rd, 2016, 5:49 pm
Forum: Student Forum
Topic: Exercise boundaries for american call and put
Replies: 21
Views: 1475

### Re: Exercise boundaries for american call and put

No, for the put (under constant interest rates), the fair value is $\max_{t \le u \le T} E[e^{-r (u - t)} (K - S_u)^+ | S_t]$, where $u$ is actually a stopping-time policy .  The optimal exercise policy is to stop at the first time after $t$ such that $S_u \le S_c(u)$. For the case ...
August 2nd, 2016, 7:36 pm
Forum: Student Forum
Topic: Exercise boundaries for american call and put
Replies: 21
Views: 1475

### Re: Exercise boundaries for american call and put

No, for the put (under constant interest rates), the fair value is $\max_{t \le u \le T} E[e^{-r (u - t)} (K - S_u)^+ | S_t]$, where $u$ is actually a stopping-time policy .  The optimal exercise policy is to stop at the first time after $t$ such that $S_u \le S_c(u)$. For the case ...
August 2nd, 2016, 12:22 pm
Forum: Student Forum
Replies: 3
Views: 622

yes, exactly, arithmetic vs compounded, what is the measure here and I assume one is a martingale under one measure but we want to price under a different one? (just making a connection to CMS convexity for example)
August 1st, 2016, 7:14 pm
Forum: Student Forum
Replies: 3
Views: 622