Questions tagged [american-options]

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Portfolio of American put option writer

I have heard that the writers of options make a portfolio in order to obtain a small risk-free profit. For an European option, the portfolio consists of a number of the underlying stock, which may ...
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2answers
45 views

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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1answer
91 views

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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84 views

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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2answers
144 views

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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40 views

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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72 views

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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73 views

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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52 views

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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28 views

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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0answers
81 views

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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1answer
70 views

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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1answer
82 views

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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1answer
83 views

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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1answer
51 views

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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101 views

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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1answer
151 views

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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1answer
117 views

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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58 views

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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27 views

Significant digits in evaluation of american options in real world

With how many significant digits are usually american options priced in real world scenarios? The only relevant question I have found on this website is this one, which requires 6-8 significant digits,...
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149 views

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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38 views

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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50 views

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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76 views

LSM Python Implementation Undervaluation Problem

I am trying to implement the LSM method in Python. My implementation leads to American put prices lower than those as reported in Table 1 of the Longstaff-Schwartz paper and in some cases they are ...
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0answers
95 views

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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1answer
158 views

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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1answer
152 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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37 views

Value american forward as american put and american call

Can I value an american forward with strike K and maturity T as the sum of a bought Call and sold Put, both american with same strike K and maturity T? If not, why?
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1answer
108 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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1answer
49 views

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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1answer
242 views

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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187 views

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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44 views

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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92 views

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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112 views

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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0answers
126 views

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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1answer
60 views

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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304 views

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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0answers
95 views

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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1answer
131 views

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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1answer
133 views

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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28 views

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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94 views

American Options in Merton's (1976) Jump Model

@LocalVolatility proves in this stellar answer that European call option prices in the Merton jump diffusion model are given by $$ C_{Merton}(S_0,r,q,\sigma,K,T) = \sum_{n=0}^\infty e^{-\lambda T}\...
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1answer
62 views

Single-period market with probability space [closed]

Let $C^E$, $P^E$, $C^A$, and $P^A$ denote prices of a European call option, a European put option, an American call option and an American put option, respectively. All of them with expiry time $T$ ...
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1answer
337 views

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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104 views

Expected life (Fugit) of American Option

How can I use the binomial tree pricing method for American options to determine the expected time of exercise for the option (or "Fugit")? In particular, how would I modify the algirithm ...
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1answer
105 views

Volatility input for American options

I have to price an american option on a daily basis and I have some questions regarding the CRR binomial tree model: Is it correct to use implied volatility as an input? Or is it better to use ...
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0answers
29 views

Deterministic optimal call time

Consider a American Option on a linear payoff i.e., if called at time $T$, it pays off $S(T)$, the stock price. Is the optimal call time of such an option determinsitc? Is there an intuition to the ...
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0answers
106 views

Option implied data from CME

I am trying to extract the risk free rate and volatility from the traded American options with expiry Nov-2020 from CME. https://www.cmegroup.com/trading/metals/...
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81 views

Option that never expires

I have been struggling with the problem below for quite some time now. I really don't know how to approach it. All I could think of is to use the Black-Scholes formula with $T \rightarrow \infty$, ...

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