All Questions
Tagged with american-options stopping-time
10 questions
4
votes
1
answer
240
views
American option pricing formulation
Assuming the usual setup of:
$\left(\Omega, \mathcal{S}, \mathbb{P}\right)$ our probability space endowed with a filtration $\mathbb{F}=\left(\mathcal{F}_t\right)_{t\in[0,T]}$,
$T>0$ denoting the ...
- 51
4
votes
2
answers
262
views
Convergence rate of Bermudan to American option
When trying to value an American option we often use grid-based methods (e.g. Monte Carlo in combination with Longstaff Schwartz; or Finite Difference Methods). As such, we are in fact estimating the ...
- 568
3
votes
0
answers
188
views
American Options in Merton's (1976) Jump Model
@LocalVolatility proves in this stellar answer that European call option prices in the Merton jump diffusion model are given by
$$ C_{Merton}(S_0,r,q,\sigma,K,T) = \sum_{n=0}^\infty e^{-\lambda T}\...
- 688
4
votes
0
answers
209
views
Boundary condition in perpetual american option problem
I am trying to solve the perpetual American option problem. Currently I'm following this (slide 9). The stock price is modelled as Ito's process.
$dS_t = (\mu-D_0)S_tdt\ +\ \sigma S_tdW_t $
where $...
- 61
8
votes
5
answers
711
views
American put option. Exercise time is a random variable, calculation of expected payoff
I got an American put option, where the payoff is $V_\tau = \max(K - X_{\tau}, 0)$ and $X_{\tau}$ is the price of an underlying at the stopping time $\tau < T$. The underlying follows a standard ...
- 273
3
votes
2
answers
374
views
Regression techniques for bermudan Monte-Carlo
One knows that the price of a bermudan claim exercisable at times $T_1, T_2,\ldots, T_N$ is $$V_0 = \sup_{\tau\in\Gamma} \mathbf{E} \left[ e^{\int_0^{\tau} r_s ds} \varphi_{\tau}\left( x_{\tau} \...
- 1,232
1
vote
0
answers
238
views
Perpetual American put option with zero interest rate
I want to find an optimal time when we should exercise perpetual American put option.
In other words I want to maximize the following equation:
$$
V(S) = \sup_{\tau \in \mathcal{\tau}}\mathbb{E}[e^{-...
- 153
2
votes
1
answer
354
views
How to solve one-touch American call
I want to solve the one-touch American call at $t = 0$ with level $B,$ maturity $T$ under the following assumption:
$$d S= rSd t + \sigma SdW,\quad S_0<B.$$
We have following formula:
$$V(S_0,0) = \...
- 1,253
0
votes
1
answer
44
views
is there a dependence between an annotation date of stocks dividend payment and the end fiscal year
I know that the fiscal year in USA from 1 October till 30 September.
I'd like to know: is whether there a dependence between a declaration date and an end of fiscal year? I think this dependence ...
- 253
1
vote
1
answer
857
views
Figure of Stopping and Continuation Region
I am reading Alternative Characterizations
of American Put Options by Carr et al. It is stated there that:
Consider an American put option on the stock with strike price $K$ and maturity date $T$. ...
