Questions tagged [american-options]
An option that may be exercised at any time before the expiration date.
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Far OTM calculation issue on Bjerksund-Stensland
Has anyone come across and fixed calculation issues on boundaries using Bjerksund-Stensland 2002 (Hull, Haug or Rouah implementations) ?
Thanks in advance
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Black Scholes/American Put/Martingale Condition
Consider a Black Scholes model with $r \geq 0$. Show that the price of an American Put Option with maturity $T > 0$ is bounded by $\frac{K}{1 + \alpha} {(\frac{\alpha K}{1 + \alpha})}^{\alpha}{S_{0}...
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American option pricing using path integrals
I am writing a brute force code in python that implements the path integral formalism for the American put option, the goal being to obtain its price at given a price $S_0$ of the underlying asset.
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Binomial option pricing model for American options on assets paying a continuous dividend yield
Let's say an asset has a continuous dividend yield of 5% (and assume interest rate is 0%). If I want to price an American call option on such an asset, I take each time step individually and construct ...
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Is it possible to have only one volatility surface for american options (that fits both calls and puts)?
Put-Call Parity does not hold for american options. Hence, I don't see how it would be possible to have one surface that would encompass both calls and puts.
For example:
Let pick a call lying in the ...
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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 ...
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Prove that there exists a critical price for a American call option with continuous dividends
For a American call option on a stock with continuous dividend yield, show that there exists a critical price, that is a price $S^*_t$ such that if the stock price is above this at time $t$, then it ...
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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 ...
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American option under Ornstein-Uhlenbeck stock price
I came across with the following problem:
For the Ornstein-Uhlenbeck process $(X_t, 0\leq t\leq T)$ with initial
condition $X_0 = x$, find the stopping time $\tau$ that maximizes
$\mathbb{E}[e^{-r\...
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implied-information in american option
I have recently been researching European options versus American options implied information. For European options, an overview article is Christoffersen(2012). But for American options, I only found ...
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How to price lookback american option when its payment is distributed during its life
I would like to price a floating strike american lookback with a particular feature: I don't want to charge upfront the client, rather I would like to insert a "running fee", some sort of a dividend.
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Is this an optimal stopping problem?
I am trying to work out how to approach a machine learning problem of 'learning' an optimal liquidation time/threshold, under some conditions, from historic data. The idea is a trader armed with this ...
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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 ...
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Delta-hedge experiment of American Put option
I am trying to run a delta-hedge experiment for an American Put option but there's a (systematic) hedge error which I cannot seem to understand or fix.
My implementation is found in the bottom of this ...
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Implied Volatility Discrepancy in American Options - Mathematical Reasoning?
I've been analyzing Tesla stock American options data and have observed an interesting pattern that I'd appreciate some help understanding.
For this analysis, I obtained the Implied Volatilities (IVs) ...
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Optimal exercise time in Binomial model
Let (B, S) a multi period binomial model that is arbitrage free.
I would like to prove that the unique optimal exercise time for an American call option is the maturity time T. My idea is to prove ...
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LSMC for Out of The Money paths
In the Longstaff & Schawartz article they condition on using In-The-Money (ITM) paths only for the regression. The reason for this is to obtain more accurate results and also reduce the ...
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Is American put Gamma always greater than the European one in the non-early-exercise domain?
Consider a pair of American and European puts with the same specifications except the former has the continuous early exercise right. Has anyone plotted the Gamma's of both as functions of the ...
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Pathwise sensitivities of American options - Derivative of the American payoff function
How can I compute the derivative of the payoff function for an American put option?
In the paper "Smoking adjoints: fast Monte Carlo Greeks" by Giles and Glasserman (2006) they compare two ...
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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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Monte Carlo American Options Discrete Dividends
Built some tree methods to price american options with discrete dividends. But I have no way to really verify my work. Questions below:
Does it make sense to build a Monte Carlo pricer to use as a ...
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Continuation value in Longstaff-Schwartz: Why the expected value?
In the paper by Longstaff and Schwartz on American option pricing, the continuation value at time $t_k$ is given by:
\begin{align}
F(\omega;t_k) = \mathbb{E}_Q\Big[\sum_{j=k+1}^Kexp\Big(-\int_{t_k}^{...
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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 ...
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Longstaff-Schwarz LS Monte Carlo - which approach is correct? [closed]
I'm trying to understand Least-Square Monte Carlo approach for pricing american options. I'm familiar with Tsitsiklis and van Roy (2001) approach where we are going backwards with:
$V_T = h(S_T)$, ...
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Comparison of the American and European call deltas
Suppose the interest rate is zero. A stock with price $S(t)$ at time $t$ pays only one dividend at time $t_1$ such that $S(s_+)=S(t_1^-)q$ where $q\in[0,1]$ is a constant. Consider a European call and ...
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If American Options always have positive time value, how can it be optimal to exercise an American Put early? [duplicate]
r > 0. I understand that money today is worth more than money tomorrow. So if volatility is 0, it's better to take the money today. But I don't understand how to square away the following:
Time ...
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How to improve fit in American options vol surface?
I am trying to model the volatility surface of index etfs (spy, iwm and qqq). I am using the CRR model with discrete dividends and the spot model. I find that for some cases there is a noticeable ...
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How to price an american put option on a dividend-paying stock? [duplicate]
There is no Black Scholes formula for the value of an American put option on dividend paying stock eithe has been produced ? Should I use the binomial model ?
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Properties of the American derivative security price process
$$
\newcommand{\cbkt}[1]{\left\{{#1}\right\}}
\newcommand{\rbkt}[1]{\left({#1}\right)}
\newcommand{\sqbkt}[1]{\left[{#1}\right]}
$$
Shreve volume I, defines an American derivative security as follows:
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Put price characterisation
I am reading Shreve's Stochastic Calculus for Finance II: Continuous-Time Models.
I am trying to understand the below two concepts:
Topic 8.3.3 Analytical Characterization of the Put price on Page ...
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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} \...
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Black-Scholes PDE for American options (inequality)
I am currently working on American options.
I saw that we can derive a PDE for American style options in the same way as with BS for European options.
In a textbook, I found that the PDE leads to an ...
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Using the SABR Model to Calibrate the Implied Volatility Smile/Surface of an American Option
If I already know the implied volatility smile/surface of an American option, can I directly use the SABR model to calibrate the smile/surface, or do I need to make certain adjustments first?
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Are "American" option strategies traded OTC?
Is there such a thing as an American butterfly spread?
For a European butterfly spread simply buying 1 put with strike price X+a, 1 put with strike price X-a and shorting 2 calls with strike price X, ...
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Time steps in CRR Binomial Option Pricing for American Options
how do you determine the time steps required as inputs to the Cox Rubinstein Binomial Option Pricing model when trying to determine the fair price of an American option? Most textbooks and literature ...
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How can I derive the price of american options given the european options prices? [closed]
I have the european volatility surface of a given asset. What is the correct procedure to compute the price of the options with american exercise type?
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What's the connection between implied vol curve of SPX and SPY?
I think there should be an obvious connection of the two implied vol curves from the SPX and SPY markets since the underlying of SPX is SP500, while the underlying of SPY is a ETF which tracks sp500 ...
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Does the risk neutral pdf that is derived using Litzenberger-Breeden Method correspond to gamma and it's integral correspond to delta?
I derived the pdf using the butterfly prices and the curve looks like gamma of an option at every strike. Is that the case or am I missing something to get the pricing of an option?
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Why is accuracy important in pricing American Options? [closed]
I see a lot of academic papers talking about accuracy in pricing American Options (and finding analytic solutions). Why is there so much interest in this topic? Isn't the option price set by the ...
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Exotic options with lookback features [closed]
I am trying to value an american call option with a lookback feature. So the holder can choose to exercise either based on a fixed strike (K) or a floating strike equal to 10-day moving average (MA). ...
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Bermudan Swaptions [closed]
Can someone explain, in layman's terms, the mechanics behind Bermudan Swapttions ( without having recourse to pricing models )?
Why are they popular? when are they used ?
How are they hedged i.e ...
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Binomial Tree for CDF
I'm tasked with solving an optimal stopping problem relating to stochastic process representing a firms profit namely $X_t = X_0 + \mu t + \sigma Wt$ where $X_0, \mu$ and $\sigma$ are constants.
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Why were Laguerre polynomials a good choice of basis functions for American Monte Carlo?
I am implementing LSMC to price American options based on a custom model. I now need to make a choice of basis functions, so I am looking for the theoretical justification for using Laguerre ...
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What are some good books to get started with option theory? [duplicate]
Recently graduated in econometrics but starting to realize my knowledge is limited. Any and all tips are welcome!
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Significant digits in numerical derivative pricing
I am looking for examples for the number of significant digits commonly required to find numerically the price different types of derivatives.
For instance, if we have to price an American put option, ...
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Perpetual Option Paying Chooser Option
A perpetual option solves the ODE
$$rSV_S+\frac{1}{2}\sigma^2S^2V_{SS}-rV=0$$
The general solution is $$V(S)=aS+bS^{\gamma}$$ where $\gamma=-\frac{2r}{\sigma^2}<0$.
For an American put option with ...
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Why do we worry about the bid/ask spread when pricing option in incomplete market?
Several resources I saw introduce the notion of bid/ask spread when trying to price options in incomplete market, I don't understand why the notion is introduced since we are interested on the price ...
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Convexity of an American put option
Is the price of an American put on an underlying without dividend convex with respect to the strike?
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Is there a closed form solution to calculate Fugit for stock options?
I am trying to find a quick and dirty way to estimate fugit for a basket of American options real time. Is there a quick way to provide a proxy? I know one can do binomial tree or monte carlos ...
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What is the optimal time for exercising American call and put option?
A 9 month American option (underlying) is known to pay dividend of USD 1 and USD 0.75 at the end of the ...
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