Questions tagged [american-options]
The american-options tag has no usage guidance.
295
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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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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 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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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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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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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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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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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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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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How to customize Leverage on a downside price Option Strategy?
How would you devise and customize a 4 Times Leverage on a Stock Price downward movement using Options, that holds the position for 1 year ? ( to do this, i know likely rolling the option would be ...
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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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Does Put-Call parity have influence over American Option pricing in practice?
I am learning my options and from what I read it seems that put-call parity is regarded as only being applicable to European options because the time to exercise is known. American options, on the ...
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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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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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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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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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How to compute the price range for an American call and put option?
A non dividend paying stock has the following details for its European option:
Time to expiry – 1 year, Risk free interest (Continuous)- 5%, Exercise price = 42, Current Stock Price = 40, Call option=...
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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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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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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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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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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:
$$\...
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Suboptimality bias in least squares Monte Carlo for American options
In Monte Carlo pricing of American options we form two estimators:
A high estimator that is biased upward because of "look-ahead" bias (i.e., at any given time we uses future information to ...
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Generating Greeks with American Options
Investor and Software Engineer but very new to quant finance here...
I have the below code (which I'm sure will be helpful for some) and have some questions regarding the function parameters!
Is RF ...
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What is the greatest theoretical delta value?
In a few options positions I'm currently holding I noticed delta values of ~0.6 while gamma is ~1.0 which surprised me as I thought delta can never be greater than 1 - meaning for every 1\$ move in ...
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Selling American calls before ex date vs. exercising
From reading Hull OFOD (among other references), I understand that early exercise makes sense for an American call option at time $t_n$ when $$D_n > K\Big[1-e^{-r\big(T-t_n\big)}\Big]$$
for a call ...
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Bermudan pricing in Black-Scholes
Is there an "analytical" method to price American options (approximated as daily Bermudans) in the Black-Scholes model using backward induction?
$$V_T(S) = \max(K-S, 0)$$
$$V_{T-\Delta t}(S) ...
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Difference in pricing of American call and put
In Paul Wilmotts quantitative finance books he says that the the value of an American option satisfies the following
$$
\frac{\partial V}{\partial t}+\frac{1}{2}\sigma^2S^2 \frac{\partial^2V}{\partial ...
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Early exercise American Options with Dividend
this is a basic question but I have not fully understood it.
Let's say we have dividend paying stock (continuous dividend yield), when would we exercise the Option early? Since the Dividend yield is ...
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Yield to call on American style callable bond
(Assuming current bond price is quoted and maturity, par value, strike price all known..)
I was wondering how do we calculate yield to call on American style callable bonds after the call date has ...
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Can a decrease in call open interest drive the stock price down?
I am analysing the price movement of a U.S. stock in conjunction with its open interest on calls vs puts. If within a month, the call open interest drastically declines (even relative to put open ...
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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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QuantLib Inaccurate - American Put Option with Discrete Dividends
I'm trying to use the QuantLib library to price American options that pay discrete dividends.
The call options are priced with good accuracy (generally <0.1% error), however the same inputs for a ...
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IV on FOP (futures options) being higher than IV on equivalent ETF
I've been observing that options on /es has a higher IV than the options on SPY even though they're both tracking the S&P 500. What causes this? Doesn't this mean that the options on /es is more ...
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BAW with deterministic rate, dividend and volatility term structures
Is anyone aware of a paper or B.Sc/M.Sc. thesis that derives the Barone-Adesi-Whaley approximation for American options with deterministic rate, dividend and volatility term structures? I have googled ...
user34971
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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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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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Valuing a call option that is issued today, exercisable after 2 years from the issue date and expires 3 years after the issue date
if we assume:
Current price: $0.25
Exercise price: $0.25
life: 3 years
Risk free rate p.a: 0.2%
volatility p.a: 85%
The option cannot be exercised within the first 2 years, after 2 years, it is ...
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How do you calculate optimal exercise boundary?
In the Broadie-Glasserman article there is a picture of simulated paths and Optimal Exercise region. How did they find this optimal exercise boudary?
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Valuing American Options using Tilley algorithm
Hey I want to implement Tilley's algorithm (Valuing American Options in a Path Simulation Model by JA Tilley, 1993) to price american options. Where can I find implementation of this method in any ...
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Least Square Monte Carlo Longstaff-Schwartz method implementation problem
While trying to implement the Least Square Monte Carlo (LSMC) method by Longstaff-Schwartz I came across an error I am not quite sure how to fix.
The method uses a regression method (be it Multiple ...
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Early Exercise of American Options on dividend-stock
I am reading the chapter 15 of Options, futures, and other derivatives by John Hull.
Specifically, 15.12 Dividends-American Call Options.
I am stuck while proving the fact that exercising an American ...
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Reason why a European binary call should be worth half of its American counterpart when driftless and out-of-the-money
Exercise 11 of chapter 8 of Mark Joshi's "The concepts and practice of mathematical finance", asks to compare prices of an American and a European digital (binary) calls when out-of-the-...
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Will an options contract always be worth more than it's intrinsic value ? Also if it's very expensive, will it be hard to sell? [closed]
So I'm wanting to know if my call option will be worth more than its intrinsic value and also if lets say it ends up being worth 20k will people be buying it on the market ?
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