Questions tagged [american-options]
An option that may be exercised at any time before the expiration date.
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Clarification on Perpetual American Call Option Valuation in "Heard on the Street"
Following the solution provided by *Timothy Falcon Crack - Heard on the Street, Quantitative Questions from Wall Street Job Interviews:
For $S \geq \underline{S} \equiv \frac{\lambda_2 K}{\lambda_2 - ...
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How do exchanges calculate IVs of American-style (stock) options?
As stated in the title, how do exchanges (such as NASDAQ) actually calculate the implied volatilities and Greeks of American-style stock options? From my perspective this is relevant if I'd like to ...
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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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Does put-call parity hold for physically settled options?
In Chapter 13 (Some Wrinkles of Option Markets) of Dynamic Hedging (pages 222-223), N. N. Taleb introduces the concept of expiration pin risk and follows by making the statement:
$\color{red}{\...
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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 ...
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implied volatility from bond futures american options
I am looking to extract implied normal yield volatility from bond futures american options.
any advice on how to tackle this?
as a separate question, what extra information does an american implied ...
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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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How to calculate the theoretical optimal Strike and Expiration for Covered Calls?
Given the following parameters:
Hold the call to expiration.
Estimate of probability of expiring ITM. (I know it is an estimate.)
Indifferent to being called away.
Only fixed number of shares ...
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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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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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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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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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recent developments in American options?
I have read the paper written by Egloff (2005) using machine learning techniques to solve the optimal stopping problem.
Is there any development in pricing American options during 2005-2016? (based ...
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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 ...
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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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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 ...
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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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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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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 ...
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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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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 ...
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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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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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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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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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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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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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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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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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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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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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