Questions tagged [american-options]
An option that may be exercised at any time before the expiration date.
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Exercising an American call option early
I have seen the rationale behind why it is never optimal to exercise an American call option early, but have a question about it.
If the option strike price is $E=\$20$ and it expires at $T=1yr$, if ...
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How to choose a risk-neutral measure when the market is incomplete?
I am more of a probabilist than a financial mathematician. I am currently working on the features of American put options under a particular stochastic volatility model.
Like most stochastic ...
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Implied Volatility from American options (binomial)
I am trying to get the implied volatility from options on commodity futures and I know it's possible to get it from the binomial american options (on an non-dividend paying stock).
I believe it is ...
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American Call: when it's European?
It is a rather well-spread fact that in Black-Scholes (BS) model for a stock with no dividends that follows Geometric Brownian Motion (GBM), the price of American call coincides with that of its ...
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When is it rational to exercise a bond option early?
Consider american options on interest rate futures such as the 10-year treasury note. When is early exercise optimal?
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Constructing Volatility Smile from American Options
My question is about best practices for reconstructing volatility smiles for a fixed tenor from American option data. For simplicity/liquidity, I am currently considering options on SPY. I am ...
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Longstaff-Schwartz (Least Squares Monte Carlo) applied to American Options
I'm working on an implementation in R of Longstaff & Schwartz method from the this 2001 article. I've managed to build code that replicates their prices in table 1 (p. 127), but only for the ones ...
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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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American Options relation between greeks
Considering an American option in a Black-Scholes model, is there a relation between Vega and Gamma as it holds in the European case?
I am aware an exact relation would be difficult to find. But in ...
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What is the industry standard pricing model for CME-traded Eurodollar future (American) options?
The CME-traded Eurodollar futures option is an American option.
What is the industry standard pricing model for this product?
Does the industry practice to treat CME-traded Eurodollar futures ...
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Issue Using QuantLib and Python to Calculate Price and Greeks for American Option With Discrete Dividends
I am having trouble using QuantLib with Python to calculate American options with discrete dividends. I am using Anaconda, Spyder, Python 3.6, and the most recent version of QuantLib. I created ...
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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 ...
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Why should an american option be exercised when its price equals its intrinsic value
Mark Joshi states :
"If the price of the american option equals its intrinsic value, we exercise and it would be an error not to do so. The reason is that once the option has been exercised, we hold ...
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Does price of american (put) option exhibit smooth pasting in time direction under B-S model?
Let us consider the BS model and let $f(s,t)$ denote the price of an American put option with $t$ to expiry, then it is known the solution of the optimal stopping (when it is risk neutral) related to ...
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Random variable minus Integral of Ito Generator is a Martingale under what conditions?
I am reading about american option pricing and the variational inequality, and the book I am reading states, in the derivation of the variational inequality, the following is a martingale: $$M_s = U(s,...
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American Swaption Heding with Malliavin Calculus
Hedging American Swaption
Hello, I priced an American swaption using Black model with swap rates diffusion to find the european (call) price at t.
$$ C_t = (\delta \sum_{j=n+1}^{M+1} Z_t^{T_j})[R(t,...
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4
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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 put for negative interest rates
It is often explained, that the rule of thumb for exercising American options is to check when the benefit from the interest rate (sell the stock earlier, get the cash, put in the bank) is higher than ...
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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-...
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Implied vol and model calibration for an american option on a dividend paying stock - is there a market standard pricing model?
In terms of calibrating a pricing model to observed prices for American options on a dividend paying stock, is there a standard way of doing this in practice?
My initial thought was to use CRR ...
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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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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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Pricing an American call under the CGMY model
I am pricing an American call under the CGMY model ($0 < Y < 1$) with strike $K$ at grid point $(x_i,\tau_j)$ where $x_i=x_{min}+i\,\Delta x $ for $i=0,1,...N$ and $\Delta x=\frac{x_{max}-x_{min}...
user16651
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Why aren't american put options martingales?
I don't understand what's wrong in the following argument.
Assume that we have a no-arbitrage market where the following products are traded:
a risky asset $S$,
a risk-free bond $B$,
an American put ...
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answer
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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-...
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Soft American Options
On Page 24-25 of N. Taleb's "Dynamic Hedging" the author talks about "Soft American Options"
A soft American option (also called a pseudo-European option) is only
subjected to early exercise from ...
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Intuition behind American Option pricing
The price of an American option is given by $$V_n = \max\left(G_n,\frac{pV_{n +1}H^d + qV_{n + 1}H^u}{1 + r}\right)$$ where p, q are the risk neutral probabilities.
I have two questions:
How can ...
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What is the point of the regression in Longstaff Schwartz method?
In the Longstaff and Schwartz method of pricing American options, what is the point of the regressions at each step?
The goal is to approximate an optimal stopping time for each path. However, why ...
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Modified bisection formula for deriving implied volatility for a dividend paying american option
I am trying to work out the formula for calculating the implied volatility of an american option on a stock paying dividends (discrete payments or annualized yield).
On page 171 of Haug
The ...
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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 ...
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Value of American Call vs Value of European Call when using implicit finite differences
I calculated values for put options (european and american) using the implicit finite difference method and compared them to black/scholes values.
The values for american put options are higher than ...
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1
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Upper bound concerning Snell envelope
Consider a non-negative continuous process $X = \left (X_t \right)_ {t\geq 0}$ satisfying $ \mathbb E \left \{ \bar X \right\}< \infty $ (where $ \bar X =\sup _{0\leq t \leq T} X_t $) and its ...
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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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Implied volatility from American options using python
I am currently trying to construct volatility surface from american option prices (using Cox-Ross-Rubinstein tree) in Python 2.7. Below you can find the code I came up with. Any corrections would be ...
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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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Least Squares Monte Carlo
Could you explain to me in words (no formulas) the concept of the Least Squares Monte Carlo method to price an American style option?
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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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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 ...
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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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How can one value a Bermudan option?
A Bermudan option allows early exercise at predefined dates, e.g. at maturity equal to $t_1$, $t_2$, $t_3$,...;
hence , would its value be the sum of 3 discounted European options with 1-year ...
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Machine learning for non optimal behaviour
I was working on the pricing of complex bermudean swaption when I noticed that the exercise is often (very) subobptimal. It seems that the clients are more sensitive to past growth or drop in rates ...
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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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Methodology for handling short american options in a back test
Given that an American option can be exercised at any time, how does one handle algorithmically shorting an American option in a back test? I am not sure what the best practice is to simulate 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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Why Vasicek model on a tree is a bad choice for pricing American option on credit prepayment?
I have an American option on a credit prepayment, i.e. the holder of the option can prepay the remaining credit if the interest rate falls below the initial strike. The pricing of this option was done ...
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Optimized search for yield-to-worst of a callable bond
Suppose that I need to find the yield-to-worst of a callable bond, and that the option is American (call any time). The bond may have step-up coupons and/or non-constant call price (oprion strike). ...
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Are radial basis functions popular in least squares monte carlo option pricing?
In a Longstaff-Schwarz setting option on several underlyings can be priced using least squares monte carlo. Using suitable set of basis functions, continuation values can be approximated using ...
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LSM American Option pricing with dividends
Under the Longstaff-Schwartz LSM method for an American call, how should I account for a continuous dividend paying stock? I assume that it'll needs to be accounted for when simulating the underlying ...
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A paradox about the American Put option price
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 ...
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Early execise of American Call on Non-Dividend paying stock.
Let us consider an American call option with strike price K and the time to maturity be T. Assume that the underlying stock does not pay any dividend. Let the price of this call option is C$^a$ today ...
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