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# Questions tagged [american-options]

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### 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 ...
79 views

### Question regarding the derivation of American Put option

When we derive the boundary conditions for the American put options, if we let $S_f(t)$ be the optimal exercise boundary, for $S \gt S_f(t)$ we get \frac{1}{2}\sigma^2S^2\frac{\partial^2P}{\partial ...
220 views

### Pricing the European counterpart from American Options

I have American option prices for SPY and need to calculate the equivalent European option price to use in further calculations. What does it (formally) mean to price the equivalent European option ...
404 views

### Use machine learning to find exercise boundary of American put option

I am working on using machine learning to obtain American Put's early exercise boundary. To train the model, I need an output label (known boundaries values). Is there a fast way to obtain the ...
1k views

### Understanding early exercise of options - The implicit put in an American call

I am self-studying for an actuarial exam on models for financial economics. I am having a hard time grasping the concept highlighted in red: I was wondering if someone could further elaborate on why ...
1k views

### Implied Dividend from American Options (in practice)

I just tried to price the implied dividend for a few active, liquid options markets using current prices and I am not convinced my results are accurate. I am using American options, and using the put-...
76 views

### Numerical American option for variable volatility

There are numerous numerical solvers for American option pricing. However, all of them take as input a fixed value sigma, denoting the historical volatility of the underlying. I am looking for a ...
60 views

### Perpetual American option price under pure random walk

Usually, American options can only be priced numerically. An important exception is the perpetual option, i.e. an American option with infinite maturity. Most mathematical finance textbooks treat this ...
93 views

### How to calculate ROI on a net credit option transaction?

If I have an option that has a net credit and results in a positive expected value (based on my own estimates of volatility), how do I calculate an ROI in order to compare with a net debit credit ...
712 views

### Least Square Monte Carlo - american Call Option

An American Call Option on an non dividend paying stock has the same value as a european one. I tired to compare the results given by the LSM with the results given by the B&S formular. It seems ...
283 views

### How to calculate return on investment for an adjustment to a complex options position?

Say I currently hold a set of options positions with the same symbol/expiry that collectively have a net present value based on the estimated value at expiration of +10. I could also liquidate the ...
208 views

### Pricing an American derivative with finite differences

I have a basic fundamental question on pricing an American option in the Black-Scholes (BS) framework: I seem to confuse two different approaches to price any early exercise, Write down a linear ...
378 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 $T$. ...
437 views

### Full value function of an American option with QuantLib FD

I am looking at the Equity Option example of QuantLib: http://quantlib.org/reference/_equity_option_8cpp-example.html and more particularly the FDAmericanEngine. However, I am not interested in the ...
70 views

### How can I drive FPDE of American Option Price from FMLS Model?

Under the risk neutral measure $\mathbb{Q}$. The FMLS model assumes that the log value of the underlying i.e., $\bar{x}_t=\ln S_t$. with dividend yield $D$ follows a stochastic differential equation ...
233 views

### pricing american put option with fdm

Assume I use some finite difference solver to solve for American type of exercise in BS framework where stock pays dividend discretely. Then at every time iteration, for call option, I firstly adjust ...
164 views

### How to calculate implied borrow rates from option chain information?

I am given information about a ticker with following options data: stock price, date, expiration date, strike price, call / put indicator, style (American or European), ask price, bid price, mean ...
113 views

### Is there any literature on a closed-form/analytical solution for American option prices with use of Chaos Theory?

I found the following paper which uses homotopy analysis for a closed-form solution. Does it have direct/apparent connections with chaos theory? http://bfi.cl/assets/zhao-wong-2006---a-closed-form-...
75 views

### Equivalent call option to the underlying stock

Would there be any benefit to an investor to purchase an American Call option on a single share with no expiration date and a strike price of 0 as opposed to purchasing the underlying zero dividend ...
106 views

### Finding optimal drift, importance sampling, least square monte carlo

I am working with Importance sampling for Least Squared monte carlo and have now problems understanding the implementation of the Robbins-Monro algorithm for finding the optimal drift for finding ...
357 views

Suppose a put option on a stock $S(t)$ following a Geometric Brownian motion is given, with strike $K$ and maturity $T$. Let us denote its price at time $t$ by $p(t,S(t))$. Now, by no-arbitrage ...
750 views

### Importance Sampling for pricing options with longstaff and schwartz

I have been asking this similar question before. However, I really want to be concrete and get and concrete explanation. I have been reading the paper by Moreni and try to implement the same ...
213 views

### How do I compute volatility and greeks of the american option on futures using matlab toolbox?

I have learned some knowledge on option pricing by myself at a very beginne level. I'm using Matlab R2009b finacial derivative toolbox. I found option pricing functions for american options on stock, ...
490 views

### Importance Sampling for Least Square Monte Carlo [duplicate]

I am currently trying to implement and model an Importance Sampling estimator for Longstaff and Schwartz algorithm for pricing American put options. It is used such that more paths are in-the-money ...
858 views

### Yahoo Finance Implied Volatility Calculation

On 5/16/16 AXP stock closed with a price of 64.07. Yahoo Finance reports an implied volatility of 20.58% for this out of the money call option: ...
120 views

I'm trying to implement Andersen and Broadie's dual method for an upper bound (here) of a regular American Put. I understand the process to compute it, but I have a conceptual issue : everything ...
206 views

### Perpetual American Put Supermartingale property

Discounted price process of an american put (perpetual) has a $dt$ part in it, which is negative if the price at time $t$ is less than the optimal exercise price. This is the only thing that drags the ...
266 views

### Isn't Black's approximation for American options inconsistent?

I have came across a formula suggested by Fisher Black (Fact and fantasy in the use of options, FAJ, July–August 1975, pp.36) for approximating the price of an American call written on a dividend-...
465 views

### Perpetual American options

Formulate and solve the free boundary problem for the perpetual American options with the following payoffs. a.) $(S - K)_{+} + a$ where $a > 0$ b.) $(K - S)_{+} + a$ where $a > 0$ ...
240 views

### Two-period binomial model for American option

Consider a two-period binomial model for a risk asset with each period equal to a year and take $S_0 = 1$, $u = 1.5$, and $l = 0.6$. The interest rate for both periods is $R = .1$. a.) Price an ...
581 views

### Solution for american perpetual put

I have been attempting an exercise in which I have to determine the value of an american perpetual put, $P$ in terms of the asset value $S$. The solution to the exercise says: When $S>S_f$ (the ...
267 views

### American option - Upper bound

I have computed a lower bound for an american option through longstaff and schwartz's algorithm. Now I have to compute the upper bound as andersen and broadie does in their article linked. Can anybody ...
392 views

### Can call options be priced with Least-Squares Monte Carlo?

I have been reading about Least-Squares Monte Carlo (using Longstaff & Schwartz algorithm) for option pricing. So far, I have only read examples that uses LSMC for american/bermudan PUT options ...
3k views

### The Upper Bound of an American Put Option

I have just read the following paragraph (in bold) and have a question on the upper bound of an american put option: http://www.sharemarketschool.com/option-valuation-upper-and-lower-bounds-part-...
2k views

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### Foresight bias in least square monte carlo

Foresight bias means we tend to over estimate the American option value. This we observe in other areas of statistics - e.g. in sample test almost always gives better prediction than out of sample ...
173 views

### Least-Square Monte Carlo in multiple variable

The paper by Longstaff-Schwatz on Least Square Monte Carlo offers very little proof. The only proof they have given assumed the option can only be exercised at two different time point and the price ...
575 views

### pricing american calls on non dividend paying stocks

It is never optimal to exercise an american call option early if it is written on a stock that doesn't pay dividends, yet when pricing such an option, using a binomial model, we check whether or not ...
73 views

### How can the time value portion of an option be higher than 100%?

Here's a screenshot from InteractiveBrokers TWS for the near-the-money put and call on the ES Dec '15 Future: The absolute value of the time value, 9.50, makes sense. But why is the percentage value ...
58 views

### Jacobian for Newton method for American options by front fixing

In this paper Penalty and front-fixing methods for the numerical solution of American option problems a front fixing method based on Newton is described for an American put option is described. I am ...