Questions tagged [american-options]

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55 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
66 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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58 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
50 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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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
64 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
85 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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57 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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26 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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124 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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35 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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45 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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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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87 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
104 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
130 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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35 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
64 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
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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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1answer
174 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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92 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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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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69 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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85 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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113 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
58 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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268 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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82 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
95 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
99 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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43 views

American put option with $r=0$ [duplicate]

What the value of American put option in the case when $r=0$ with the payoff $\max(K-S(T),0)$, by using the Snell envelope Theorem? Snell envelope theorem: the optimal value process $V$ is the Snell ...
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24 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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78 views

Portfolio of American Binary Option and Knockout Option

Assume I have a portfolio where I long an American Perpetual Binary option (that pays 1 if S>=K and 0 otherwise) and I short a knock out barrier option. This ...
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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
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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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61 views

Determining the early exercise curve of an American option

When I have found the price of an American option using, say, a finite difference scheme - how do I find the early exercise curve from this solution? Here is my idea: What I have is the price of the ...
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1answer
287 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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84 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
91 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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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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93 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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0answers
66 views

Early exercise premium with discrete cash dividends using integral approximation

From my understanding, we have to integrate $N(d1(S_x-D,B,t))$ on both asset-price and time-space to derive the Early Exercise Premium $EEP(B,t)$ on each $t$ before the ex-date to get current early ...
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1answer
79 views

Can a down-and-out barrier call option be priced using the Black & Scholes formula or should it be approximated?

I am trying to price of a Down-and-Out Barrier call option with leverage. When the price of the underlying asset hits a certain barrier (B), the option becomes worthless. The issuer of these options ...
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43 views

The wider bid-ask spread of in-the-forward American option

Why is the bid-ask spread of a in-the-forward/money American call (put) much larger than the out-of-the-forward/money American put (call)? I suppose the answer to the same corresponding question ...
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1answer
93 views

Option data analysis

This question is regarding the following tweet: https://twitter.com/yuriymatso/status/1281730109141954561 How was the original tweeter able to know that "Someone made a ...
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Confusion about American style option

In American style exotic options, the holder is often faced with choices at certain times during the life span of the option. Following the/an optimal choice allows the user to maximize the value of ...
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1answer
416 views

Converting an American option to European option [closed]

I wonder if there are any websites/resources/sample codes/papers on how to convert the American options to European options (when all else are equal). i.e. if given same underlying asset, same ...
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1answer
63 views

Convexity of a rates Bermudan w.r.t strike

Recently there was a nice question asked on convexity of American put w.r.t strike: Convexity of an American put option Does the same hold for a Bermudan option in rates, where they underlyings are ...
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1answer
243 views

Under what conditions will both European and American put options worth the same?

It is well-known that on a non-dividend paying stock, it is suboptimal to exercise an American call option earlier. In other words, both European and American call options on the same non-dividend ...

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