Questions tagged [american-options]

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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
33 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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135 views

How to compute standard errors of an estimator with antithetic variates?

I'm pricing American options using Longstaff and Schwartz Least square method. When using the following Python code, I obtain nearly the same prices and standard errors as in the Valuing American ...
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1answer
41 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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96 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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56 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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23 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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55 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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44 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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97 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
56 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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266 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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63 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
52 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
48 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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42 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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23 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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72 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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81 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
60 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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55 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
200 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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59 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
74 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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28 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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57 views

Deriving American option greeks

I am using integral representation of option value instead of trees, so I imagine to derive greeks we have to integrate across time for the boundary to get the EEP (Early Exercise Premium) component ...
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87 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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80 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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60 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
65 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
91 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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55 views

Early exercise boundary for american call and discrete cash dividend boundary approximation

I am attempting to derive early exercise boundaries for American calls paying both continuous and fixed discrete dividends using the combination method from integral equations. I have successfully ...
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48 views

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
331 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
57 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
156 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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1answer
117 views

Inequality involving Co-Terminal/Co-Initial American vs Bermudan Swaptions

Let us consider a payment schedule $\mathcal{P}:=\{t_1,\dots,t_n\}$ which has a corresponding fixing schedule $\mathcal{F}:=\{t_0,\dots,t_{n-1}\}$. We have a series of co-terminal and co-initial swaps ...
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1answer
109 views

Estimating optimal exercise boundary for an American call by LSM method

I'm trying to derive optimal exercise boundary using LSM method and got some weird outcome. So, I evaluated an American call option by LSM method and now need to find the optimal exercise curve. Do I ...
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17 views

What does it mean to change the initial average value to asset an asian-american option?

I am currently trying to replicate the Longstaff (2001) paper where he explained the least-squared approach to value American options. In section 4, he explained how to apply this method to asset a ...
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3answers
728 views

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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1answer
87 views

Far OTM calculation issue on Bjerksund-Stensland

Has anyone come across and fixed calculation issues on boundaries using Bjerksund-Stensland 2002 (Hull, Haug or Rouah implementations) ? Thanks in advance
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110 views

Boundary condition in perpetual american option problem

I am trying to solve the perpetual American option problem. Currently I'm following this (slide 9). The stock price is modelled as Ito's process. $dS_t = (\mu-D_0)S_tdt\ +\ \sigma S_tdW_t $ where $...
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1answer
91 views

Arbitrage between American and European put options on the same underlying asset

Suppose there exist both American-style and European-style put options on the same underlying asset, at the same strike price, and with the same expiry date. Suppose the European put is selling below ...
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1answer
388 views

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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37 views

Does the price of an American Put often exceed the Payoff?

According to shreve the value of a put is equivalent to or greater than the possible payoff, before a stopping time with the condition that its value equals the intrinsic value. First what does it ...
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1answer
30 views

Reference for “an increase in volatility increases value/price of american options”

I'm looking for a textbook/journal article reference for the well-known result that an increase in volatility increases the value/price of a standard American (call and put) option. In the case of ...
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113 views

delta of synthetic forward of american options

For european options, we know the delta of a synthetic forward position (long call short put with the same strikes and maturities) because of the put-call parity. However the P-C parity does not apply ...
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24 views

How to calculate strike price for an American put given its value at time 0 and the binomial tree of stock prices?

Given the interest rate, prices of the stock at time 0,1,2 where T=2 is the expiry date, and the value of the American put at time 0, how do I calculate its strike price? The question gives it the ...
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1answer
74 views

Create a Synthetic Single Stock Future

Is it possible to create a synthetic long single stock future using the stock and it's vanilla options with the caveat that selling naked puts is NOT allowed? That is, you can write puts, but they ...

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