- January 25th, 2018, 11:17 am
- Forum: Student Forum
- Topic: Optimal exercise boundary at expiration...
- Replies:
**4** - Views:
**1191**

there's a standard explanation obtained by substituting the pay-off (S-K) at expiration into the PDE and looking at the sign of [$]\frac{\partial V}{\partial t}[$] at expiration [$]\frac{\partial V}{\partial t}=-\frac{S^{2}\sigma^{2}}{2}\frac{\partial^{2}V}{\partial S^{2}}-(r-D)S\frac{\partial V}{\...

- January 24th, 2018, 4:23 pm
- Forum: Student Forum
- Topic: Optimal exercise boundary at expiration...
- Replies:
**4** - Views:
**1191**

According to Kim (1990, p.560) in "The Analytic Valuation of American Options". https://imgur.com/a/kua3M I understand the first minimum condition where K sets the lower bound of the optimal exercise boundary at expiry, but the second one is unclear to me, Update: $\delta$ = divdend rate, risk-fre...

- May 30th, 2017, 11:25 am
- Forum: Numerical Methods Forum
- Topic: Finite difference method for early exercise boundary specifically
- Replies:
**28** - Views:
**2884**

As mentioned, there is no 'simple' FDM for this IMO. And since this is a nonlinear problem then accuracy is first-order, all things being equal. Or use front-tracking. LIke this http://docs.lib.purdue.edu/cgi/viewcontent.cgi?article=2287&context=cstech It's trickier than usual FDM but is doable. E...

- May 29th, 2017, 10:05 pm
- Forum: Numerical Methods Forum
- Topic: Finite difference method for early exercise boundary specifically
- Replies:
**28** - Views:
**2884**

It's highly accurate for most cases (I expect 6 digits here), but there are exstreme-ish parameter configurations where it blows up. I would still need to quantify that region before I would use it in production. It's the method described in this paper " High Performance American Option Pricing, An...

- May 29th, 2017, 9:26 pm
- Forum: Numerical Methods Forum
- Topic: Finite difference method for early exercise boundary specifically
- Replies:
**28** - Views:
**2884**

It's highly accurate for most cases (I expect 6 digits here), but there are exstreme-ish parameter configurations where it blows up. I would still need to quantify that region before I would use it in production. It's the method described in this paper " High Performance American Option Pricing, An...

- May 29th, 2017, 8:44 pm
- Forum: Numerical Methods Forum
- Topic: Finite difference method for early exercise boundary specifically
- Replies:
**28** - Views:
**2884**

is your method extremely accurate?. Just want to get a feel for your boundary compared to FDM or any other numerical method.

- May 29th, 2017, 8:28 pm
- Forum: Numerical Methods Forum
- Topic: Finite difference method for early exercise boundary specifically
- Replies:
**28** - Views:
**2884**

would it look different if You had used FDM to create it?

- May 29th, 2017, 7:44 pm
- Forum: Numerical Methods Forum
- Topic: Finite difference method for early exercise boundary specifically
- Replies:
**28** - Views:
**2884**

My value is very close " 8.94366" Did you attain those values using FDM ? Also, I maybe asking for a lot here but, your plot is exactly what I want but I would like the dots to be more connected (a line between them maybe? ) so the boundary the depicted would be almost like a continuous function...

- May 29th, 2017, 6:10 pm
- Forum: Numerical Methods Forum
- Topic: Finite difference method for early exercise boundary specifically
- Replies:
**28** - Views:
**2884**

Hi i been looking around the net for a Finite difference script/routine (For Matlab, c++, python) which specifically can depict the early exercise boundary for an American put with the following inputs: S = 100 K = 100 r = 0.08 volatility = 0.2 dividend = 0.04 T = 3.0 dt = 0.03 I want the routine to...

- May 15th, 2017, 7:26 pm
- Forum: Student Forum
- Topic: Backward Recursion
- Replies:
**0** - Views:
**486**

Can someone explain how they do get Bt values using this backward recursion ?

It is related to the uploaded picture..

It is related to the uploaded picture..

- April 21st, 2017, 9:21 pm
- Forum: Student Forum
- Topic: Why changing measure is necessary?
- Replies:
**23** - Views:
**2422**

I want to understand the logic for why this is: We have our model for the stock price behaviour: $$d{S_t} = \mu {S_t}dt + \sigma {S_t}d{\tilde W_t}$$ It describes the development of a stock price over time using the risk-adjusted expected return $\mu$ and the real uncertainty in the stochastic term....

- April 20th, 2017, 4:59 pm
- Forum: Student Forum
- Topic: How can i derive this first passage probability formula
- Replies:
**8** - Views:
**1146**

Possible typo in first passage probability formula? The first passage probability given by Bunch and Johnson is given as $$Z = {1 \over \sigma }\left[ {\log {S \over {Sc}} + (r - {1 \over 2}{\sigma ^2})t} \right]$$ after reading some literature should it not be the case that the first passage probab...

- April 20th, 2017, 11:47 am
- Forum: Student Forum
- Topic: How can i derive this first passage probability formula
- Replies:
**8** - Views:
**1146**

I wonder if it is derived from $$Z = \exp \left\{ {\sigma X(t) + (\sigma r - {1 \over 2}{\sigma ^2})t} \right\}$$ where $$X(t) = \log S/Sc$$

- April 19th, 2017, 5:34 pm
- Forum: Student Forum
- Topic: How can i derive this first passage probability formula
- Replies:
**8** - Views:
**1146**

can you write it more clearly?

- April 19th, 2017, 4:06 pm
- Forum: Student Forum
- Topic: How can i derive this first passage probability formula
- Replies:
**8** - Views:
**1146**

In this article the authors present this first passage probability formula $$Z = {1 \over \sigma }\left[ {\log S/{S_t} + (r - {1 \over 2}{\sigma ^2})t} \right]$$ ${{S_t}}$ value of the stock at time t , r ror on the stock, $\sigma $ standard deviation. The authors ref. Feller (1971) "An Introductio...

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