# Questions tagged [american-options]

An option that may be exercised at any time before the expiration date.

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### Difference in value - American call and a European call - stock pays a dividend

For a stock paying a single dividend prior to expiration, I would like to estimate the difference in value between an American call and a European call with the same expiration, strike and underlier. ...
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### American option PDE [closed]

I'm reading the pdf here regarding the PDE associated with the American option. Essentially, one would turn the Black Scholes PDE into an inequality. Suppose you're pricing an American put where $S$ ...
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### Upper Bound on European/American Call Option (Hull)

I recently began reading Hull's derivatives textbook, and found a line that he didn't expand on much. Let $c$ be the price of a European call, $C$ be the price of an American call, and $S_0$ be the ...
47 views

### Implied Vol under CEV model

Consider the following steps: Suppose the underlying equity follows a CEV model $dS_t = rS_t dt + \sigma S^{0.5} dW_t$. Use the above CEV model to simulate Monte Carlo paths and price a large set (...
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### Ideas behind early exercise of American Option

In Dynamic Hedging by Taleb, there is an example at pag 24-25 about early exercise of American options, already present here, but without a clear explanation, at least for me, about the cost/...
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1 vote
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### Early exercise with multiple dividends

I am wondering how early exercise conditions work on multiple dividends. Say a stock pays 4 dividends in a year. We are 1 day before the first ex-div date and long an ITM Call and ITM put in an expiry ...
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### Unable to correctly implement the pricing of an American call with multiple discrete dividends using the Clenshaw-Curtis quadrature

I'm not a quant, just an enthusiast. I am trying to implement in C++ the methodology published in the paper "Fast Quadrature Methods for Options with Discrete Dividends", by Thakoor and ...
1 vote
37 views

### Regress later LSMC

I am looking at the regress-later LSMC introduced by Broadie, Glasserman Ha. This can be found here: Simulation for American Options: Regression Now or Regression Later? by Paul Glasserman and Bin Yu ...
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### What are the downsides of using Kim's integral equation (1990) to determine the exercise boundary of an American option?

I'm new to the industry and trying to wrap my head around American options pricing. The integral equation(1) from Kim (1990) doesn't seem to make any strong assumptions, and approximating the integral ...
1 vote
53 views

### Improvement in lower bound of American call with discrete dividends

Question Suppose a stock pays 2 discrete dividends $d_1, d_2$ at times $t_1, t_2$ respectively, where $t < t_1 < t_2 < T.$ Assume the risk-free rate, $r$, is a positive constant. Given that ...
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### JDOI variance reduction method python

Has anyone read the paper 'JDOI variance reduction method and the pricing of American-style options' by Johan. I want to implement the simulation. But For Monte carlo I got different results. andI ...
1 vote
298 views

### Longstaff & Schwartz algorithm - Python: American option cheaper than European option

I have implemented the Longstaff & Schwartz algorithm for pricing American Option in Python, but I ran into an issue while doing some experiments: sometimes, for the same option, I get a higher ...
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### Understanding American option payoff at T+0

The above picture shows the payoff at expiry(in gold) and at current time T+0(in blue) for a bull call spread. I am trying to understand American options and to know if it has any significant ...
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### Early exercising American put options

I have found a proof that an American put option without dividend will never be exercised early. However, I suspect that that is not true, so there should be a mistake in the proof. The proof is as ...
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1 vote
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### Under put call parity shouldnt the implied volatility for call and put for same strike and maturity be the same?

If all of the other inputs into black scholes (divs/rates/time to maturity/strick/current price/etc) are all the same between two pairs of calls/put contracts on the same security, shouldn't the ...
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1 vote
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### Volatility of American vs European Stock option return

Let's say that I hold an American Call Option (ACO) and an European Call Option (ECO) in my portfolio on the same underlying, with same strike price and same maturity date. Given that I hold both ...
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### American Option Valuation - Induction algorithm

The price of an American put option is given by $$V_k = \sup_{\tau\in\mathcal{T}, \tau\ge t_K} E\{e^{-\int_{t_k}^\tau r_sds} (K-S_{\tau})^+|\mathcal{F}_{t_k}\}$$ I found in one book the following: \...
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### Suboptimality bias in least squares Monte Carlo for American options

In Monte Carlo pricing of American options we form two estimators: A high estimator that is biased upward because of "look-ahead" bias (i.e., at any given time we uses future information to ...
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