Questions tagged [american-options]

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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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How to get forward curve from American options

I am curious about how one could derive the forward price for a given tenor when dealing with American options? Since with American options put/call parity is only an inequality that must be satisfied,...
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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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Optimal exercise of American BOND option

I know that early exercise for American options has been discussed extensively, but I have not seen a lot in relation to BOND options with American optionality and there are few things I cannot get it ...
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2 votes
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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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0 votes
1 answer
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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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1 answer
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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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1 answer
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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 ...
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1 vote
1 answer
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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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9 votes
1 answer
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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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1 vote
1 answer
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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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3 votes
1 answer
183 views

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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1 vote
1 answer
150 views

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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1 vote
1 answer
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American options and stopping times

The price of an American put option can be written as the following optimal stopping problem: $V(0) = \mathop {\sup }\limits_{\tau \in \mathcal{T}} {\mathbb{E}^\mathbb{Q}}\left[ {{e^{ - r\tau }}\max [...
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What does the theta curve of an american option look like?

Is the theta decay curve you see often given around the internet below in fact valid for American-style options? Often times, calculations for European-style options (Black-Scholes) are passed off as ...
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Local vol vs stochastic vol in the context of American digital options

I have two models of some spot. One is under local vol and the other is under stoch vol. Both are calibrated to the prevailing vanilla prices. I then consider the option that pays $1$ if the spot ...
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Longstaff and Schwartz example in their paper

I was looking at the well known Longstaff and Schwartz paper "Valuing American Options by Simulation: A Simple Least-Squares Approach". There are a couple of examples where they applied the ...
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Extracting implied dividends from American options

I am using end of day options data and want to extract discrete dividend information contained in the option prices. I am doing this for ETFs like SPY where I know the dividend schedule. These are the ...
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2 votes
0 answers
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How to price a Perpetual American Put Option with the Binomial Tree Model?

How do we price an American Put Option with simplified assumptions of non-zero interest rate but zero volatility and zero dividend rate? I understand the concept of Perpetual American Options and I ...
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1 vote
1 answer
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Why might Implied Volatility continue stay elevated even after binary event?

After the Georgia Senate runoff results were called today (Jan. 6, 2021), I had expected the IV on many election-related tickers to fall. In other words, I thought a major IV crush was in the cards. ...
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4 votes
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FX American call option optimal exercise and holding region

Problem I am considering an American call option which gives a domestic investor the right to buy a unit of foreign currency at a strike of $K$ units of domestic currency. I have an exchange rate $S_t$...
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1 vote
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Practical implementation of Vellekoop-Nieuwenhuis model/interpolation

Have read the 2006 VELLEKOOP-NIEUWENHUIS paper (Efficient Pricing of Derivatives on Assets with Discrete Dividends) (Download) many times re Discrete dividends on American Options, but remain baffled ...
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Constructor error pricing american ops with divs quantlib?

Looking at post from Issue Using QuantLib and Python to Calculate Price and Greeks for American Option With Discrete Dividends and trying to recreate the result; but getting a constructor error I ...
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1 answer
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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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0 votes
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Seed Values guaranteed convergence of Implied Volatility Calculation

Looking for good seed values for Newton Raphson to guarantee convergence of implied volatility calculation for a few models, all of which are for equities that have divs. 1) Bjerksund-Stensland 2002; ...
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