Questions tagged [american-options]

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Arbitrage price and American option

I'm studying American Options. If I have $X=(X_n)$ an American option, it is not possible to determine a self-financing predictable strategy ($\alpha, \beta$) that replicates the option in sense that $...
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20 views

Why does an American option on a continuous dividend paying stock have a critical price above which it is optimal to exercise early?

An American call on a continuous dividend paying stock must be above its intrinsic value, i.e $c(t)\geq\max(S_t-K,0)$. Why is there a critical price above which it is optimal to exercise (i.e. we ...
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47 views

What is the reason that an American option has a lower volatility than an European counterpart?

I was researching some plain vanilla option American/Option data and I found some European option which are more expensive than there American counterpart (all other factors are equal, except for the ...
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51 views

American Perpetual Put Option

I want to compute the expected payoff of a (classical) perpetual American put option in the Black-Scholes-Merton (BSM) framework with an optimal strategy of exercising the option at time $\tau=\inf\{t:...
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1answer
61 views

American Put Option Pricing

I am trying to solve a question of American Put Option pricing as below. Build a 15-period binomial model whose parameters should be calibrated to a Black-Scholes geometric Brownian motion model with:...
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1answer
98 views

Least Squares Monte Carlo

Could you explain to me in words (no formulas) the concept of the Least Squares Monte Carlo method to price an American style option?
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65 views

Valuation of Callable Bonds

Is there any way to price American Callable Bonds (those which can be called on any date before expiration) other than basic CRR interest rate trees, since they won't be accurate enough to give ...
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58 views

Fast implied volatility for american options

Peter Jäckel has developped a method to compute implied volatilites from option prices, called "by implication", see the papers : By Implication Let's be Rational on its website -- as well as a ...
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71 views

What are the main problems for calculating the implied volatility of in the money American put options?

As stated in the question I have a problem with calculating the implied volatility for in the money put options I have a data set of 2.6 million American style plain-vanilla call and put options. For ...
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16 views

Longstaff Schwartz with future conditional coupons

I've implemented the L-S algorithm for a simple put option. I want to value a more complex derivative which has future conditional coupons which only occur if the option is in the money. How would I ...
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1answer
74 views

Longstaff Schwartz algorithm

I am new in finance, I have implemented the Longstaff Schwartz algorithm for pricing american otion - one asset (dimension = 1). My questions : Does this algorithm still efficient for a high ...
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1answer
71 views

Why do we have to use in-the-money paths in LSMC, and how?

In Longstaff's original LSMC paper (Valuing American Options by Simulation: A Simple Least-Squares Approach, 2001 (link)), it is claimed that one should only use in-the-money paths for regression at ...
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41 views

Free Call Option [duplicate]

Suppose we follow the assumptions of the Black-Scholes Model, including unlimited borrowing, continuous prices, and frictionless markets. For simplicity assume the risk-free rate is 0. In this world, ...
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1answer
70 views

Solving for Implied Volatility Vega gets stuck at 0 (Python)

So my goal is to calculate option greeks with as few manual inputs as possible. I managed to get the IV for at the money options but then when I try further OTM strikes my results get completely ...
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1answer
117 views

American put option. Exercise time is a random variable, calculation of expected payoff

I got an American put option, where the payoff is $V_\tau = \max(K - X_{\tau}, 0)$ and $X_{\tau}$ is the price of an underlying at the stopping time $\tau < T$. The underlying follows a standard ...
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1answer
88 views

Finite difference methods for (continuously) strike-resettable American options

For simplicity, let us consider an American call/put with a continuously resettable strike price. Current time is $t=0$, maturity is at $t=T$, and the initial strike is $K_0$. We consider a "...
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2answers
80 views

American Option Exercise

Suppose I am a market maker in American options. At end of day I have positions in various options but my portfolio is overall hedged. Now, after the market close, someone decides to exercise an ITM ...
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1answer
141 views

Monte Carlo Method for American Call Option (No Dividends)

I tried to pricing the American Call option using "Longstaff-Schwartz" least squares method. However, I found the American call option is always lower than the Monte Carlo European call option (they ...
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45 views

What is the true “value” process of American derivatives?

Consider a continuous-time market where LOOP (law of one price) holds. The first fundamental theorem of asset pricing states explicitly that in the absence of arbitrage, the risk-neutral measure ...
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33 views

American-Bermudan-Asian option fixed strike using finite differences

I'm trying to price the same American-Bermudan-Asian option described in Longstaff Schwartz (2001). Specifically, using finite difference methods with an explicit scheme to solve $\begin{aligned} \...
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108 views

Longstaff-Schwartz, special american option simulation using Python (numpy package)

I got a put option, which can be exercised 3 times, all at different times, which are each month of a year $$t_1 = \frac{1}{12}, t_2 = \frac{2}{12} ... t_{12} = 1$$. Respectively, if exercised at $$...
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2answers
108 views

Is American option price lower than European option price?

I used to think under the same condition, the American option is always more expensive than the European option, because American option can be exercised at any time (has more rights than European ...
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72 views

Greeks Intraday Characteristics and PnL of options

I am modeling intraday and short term options on Futures.Think Monday, wednesday, friday contracts on these tickers: ES, NQ, CL, ZN, ZF, NG. I am wondering about documentation for Intraday greek ...
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108 views

Random variable minus Integral of Ito Generator is a Martingale under what conditions?

I am reading about american option pricing and the variational inequality, and the book I am reading states, in the derivation of the variational inequality, the following is a martingale: $$M_s = U(s,...
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17 views

Benchmark values for exotic options with highly nonlinear boundaries

I have created some modifications of least squares monte carlo algorithm for pricing american options which gives me lower and upper bound. Now I want to test how good it works for options with highly ...
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105 views

Binomial Model Implementation Trouble - American and European options come out equal

I'm Trying to implement the binomial option price model in python and get reasonable performance by using memoization. I checked the output against a black and scholes model and for European options ...
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1answer
77 views

Pricing an Asian style forward contract with early exercise feature

Is there an analytic way to price or approximate a contract with payout $A_t - K$, where $A_t$ is the running average price of the underlying asset from $[0, t]$ and $K$ is (fixed) strike. If this ...
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1answer
57 views

Pricing American style Asian option

Is there any approximation of American style Asian option (with strike equal to the running averaging from 0 to $t$) pricing based on analytical closed form formula? I see the price difference ...
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2answers
351 views

Least-Squares-Monte-Carlo by Neural Network Estimator for pricing American Option Python [closed]

First I did the LSM (Longstaff-Schwartz) to understand how its work to price an American option. code for standard_normal ...
2
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1answer
79 views

Regression techniques for bermudan Monte-Carlo

One knows that the price of a bermudan claim exercisable at times $T_1, T_2,\ldots, T_N$ is $$V_0 = \sup_{\tau\in\Gamma} \mathbf{E} \left[ e^{\int_0^{\tau} r_s ds} \varphi_{\tau}\left( x_{\tau} \...
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1answer
101 views

Implied volatility for American options- time to expiration?

I am trying to compute the implied volatility of the OBM contract (on Euronext), using R, and I was wondering if, for the time to maturity, I should put the time until the contract expires or the time ...
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1answer
122 views

What is this function in the Longstaff-Schwartz paper?

$F$ is the conditional expectation function (the "continuation value") and our approximate of this using $M$ basis functions is $F_M$... but in the paper, they have this theorem: What is $F_X$? It ...
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57 views

What is meant by “replicating an American option”?

What does it mean to say that we "replicate an American option" in the usual structure of an asset-pricing model with a measure Q? I mean, any portfolio with an adapted and self-financing strategy ...
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1answer
93 views

Perpetual Put vs European Put

I am looking at a perpetual put option where the strike price is initially the stock price $K(0)=S(0)$ (i.e. at the money), but the strike price grows at the constant risk-free rate $r$ [i.e. $K(t)=S(...
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66 views

AFV Model Implementation for Convertible Bonds

I am reading the original AFV model paper for pricing convertible bonds. https://cs.uwaterloo.ca/~paforsyt/convert.pdf The paper is very technical and I am having trouble finding the actual PDE's to ...
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1answer
265 views

Why should an american option be exercised when its price equals its intrinsic value

Mark Joshi states : "If the price of the american option equals its intrinsic value, we exercise and it would be an error not to do so. The reason is that once the option has been exercised, we hold ...
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1answer
753 views

What is the point of the regression in Longstaff Schwartz method?

In the Longstaff and Schwartz method of pricing American options, what is the point of the regressions at each step? The goal is to approximate an optimal stopping time for each path. However, why ...
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1answer
99 views

Pricing an option with sparse data, high underlying volatility and returns

I'm currently pricing American and European options on an underlying with sparse data (interpolated), high annual volatility and returns over the last year around 300%. The product isn't similar to ...
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0answers
246 views

Longstaff Schwartz Algrorithm in R

I recently discovered the LSMonteCarlo library in R which basically determines the price of American options via Longstaff Schwartz method. I tried the ...
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1answer
245 views

Bermudan Swaptions

Can someone explain, in layman's terms, the mechanics behind Bermudan Swapttions ( without having recourse to pricing models )? Why are they popular? when are they used ? How are they hedged i.e ...
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75 views

Prove that the value of a perpetual American put is time-independent

I know that the value of a perpetual American put is time-independent. I think it is very intuitive property and it results from the fact that we do not have any expiry date. My question is: Is it ...
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1answer
105 views

QuantLib: How to change polynomial order in MCAmericanBasketEngine?

My goal is to price American basket put options using the Least squares Monte Carlo, or Longstaff-Schwartz algorithm. I currently have the one-dimensional case working with the Python file below (I ...
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1answer
275 views

Pricing perpetual American put option when interest rate is equal to 0

Let us consider perpetual American put option with interest rate: $r = 0$. The Black-Scholes equation in this case has the form: $$ \frac{1}{2} \sigma^2 S^2 \frac{d^2 V(t, S)}{dS^2} + (r-d)S \frac{dV(...
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1answer
195 views

Software for American basket option pricing using Longstaff-Schwartz/Least Squares Monte Carlo method

Is there free software (preferably in Python) that computes American basket (high-dimensional!) option prices in the Black Scholes model using the Longstaff-Schwartz algorithm (also known as Least ...
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121 views

Perpetual American put option with zero interest rate

I want to find an optimal time when we should exercise perpetual American put option. In other words I want to maximize the following equation: $$ V(S) = \sup_{\tau \in \mathcal{\tau}}\mathbb{E}[e^{-...
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2answers
118 views

General questions about american options

I'm currently reading about how to value an american option and I have a few questions about it. Would be very grateful if anyone can spare the time and answer them. $1)$ Since an american put and a ...
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1answer
121 views

QuantLib: Unusual point in American option volatility smile

I have a set of American options, for which I got the implied volatility thanks to the package "RQuantLib". I then used splines to interpolate my implied volatility as a function of my strikes. ...
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1answer
90 views

R script for Leasts Square Monte Carlo. How to explain vol and mean?

I am trying to do a Least Squares Monte Carlo in R. I don't know if it is the right place to post this, but I am out of options. I don't understand the following ...
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0answers
108 views

American options — doing better than Black's approximation when $r = 0$

I am trying to find the implied volatility smile for an American call option with a known dividend during the option tenor. For the sake of argument, let's say today is Jan 1, the dividend $D$ is paid ...
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1answer
133 views

Using return on equity instead of risk free rate when pricing an equity call option

I am currently a second year university student studying business, so excuse my lack of knowledge regarding the subject. I am currently studying the binomial options pricing model, which involves ...