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Questions tagged [american-options]

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36 views

How to prove that an American option does not induce arbitrage?

I have proven that the American option must be valued at $S_0$, where $S$ is the snell-envelope of the discounted payoff of the option, otherwise there would be arbitrage. However, this does not ...
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16 views

When it comes to American options, is this what is meant by largest and smallest optimal stopping times?

As I understand it, we exercise our options optimally if we do it as soon as the payoff is greater than the continuation value. So what is all this stuff about "largest" and "smallest" optimal ...
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1answer
101 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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0answers
34 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 ...
2
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1answer
65 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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0answers
38 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 ...
6
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1answer
216 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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0answers
67 views

Hedging Strategy Perpetual American Put

According to Shreve (Stochastic Calculus for Finance II ), the perpetual american put needs to satisfy two conditions : Intuitively speaking, the first one reflects the fact that the value of the ...
2
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1answer
124 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
88 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
59 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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0answers
47 views

If an American call option is valued at $V_t = \max\{ \text{payoff}_t, E V_{t+1}/(1+r)\}$, is it always the latter?

So I am told that we value American call options at time $t$ using $V_t = \max\{ \text{payoff}_t, E V_{t+1}/(1+r)\}$ Will this always be equal to $E V_{t+1} /(1+r)$ if there are no dividends?
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1answer
128 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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0answers
38 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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0answers
40 views

American option - Black Scholes equation

I know that the Black-Scholes equation for an American option should satisfy the following inequality: $$ V_t + \frac{1}{2}\sigma^2 S^2 V_{SS} + r S V_S - rV \leq 0. $$ Actually we have 3 ...
2
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1answer
56 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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0answers
30 views

Pricing perpetual Amercian put option with negative interest rate

I consider perpetual American put option with negative interest rate $r<0$ and dividend $d$. The Black-Scholes equation has the form: $$ \frac{\sigma^2}{2}S^2 \frac{d^2 V(S)}{dS^2} + (r-d)S \frac{...
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1answer
118 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
89 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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0answers
35 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
77 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
87 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
77 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
32 views

Explicit finite difference solution of the diffusion equation

Does anyone know where I could find a numerical example of how the explicit/implicit finite difference methods can be used to evaluate the value of an option for both European and American styles. I ...
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0answers
93 views

Arbitrage Strategy Long American Call and Short European Call

We know for the fact that the holder of an American call option has all the same rights as the holder of a European call option and more. This also results in American call option always worth at ...
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0answers
66 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
130 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 ...
2
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2answers
221 views

Why it is not possible to price American perpetual call option using PDE approach?

Using a standard PDE approach to price an American perpetual put option I obtain that the price of such option has the following form: $$ V(S) = A S + B S^{-2r/\sigma^2}. $$ And then I need to find a ...
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1answer
53 views

Are perpetual american options traded on real stock exchanges?

I am looking for any information about perpetual american options from practical point of view? Are they traded on stock exchanges? Do investment banks deal with such products?
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0answers
36 views

Compound option on basket of swaptions

Consider $n$ European Swaptions $S^n$ with exercise dates $T_1 < \dots T_n$. These Swaptions can have different parameters: in particular different strikes, different interest rates, different ...
0
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1answer
80 views

Optimal exercise boundary at expiration

According to Kim (1990, p.560) in "The Analytic Valuation of American Options". I understand the first minimum condition where K sets the lower bound of the optimal exercise boundary at expiry, but ...
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0answers
50 views

Did i miss something on the American put option problem?

Maybe this is a stupid question, i dont know, anyhow i recently read this part from an article, Can someone explain the part " American put value function ...and the exercise boundary jointly solve ...
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1answer
60 views

Put price, payoff, how come? [closed]

From Merton (1973) the following boundary condition is valid for an American put. G(S,t:E) >= Max [0,E-S] I dont understand how the Rational put price can be ...
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0answers
34 views

Merton (1973) and the difficulty in pricing American put option

How did Merton (1973) realize that the methodology of Black and Scholes (1973) could not be applied to the valuation of American put options?
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29 views

American put PDE

How does the partial differential equation governing the American put look like if the stock pays dividends? Including the boundary conditions, which would be nice to get a simple explanation on.
0
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1answer
139 views

Am Call = Euro Call if r is non-negative and Am Put = Euro Put if r is negative

It can be proven that under non-negative interest rates, it is never optimal to exercise an American call option, such that: We know, if R >= 0, the current price C of a Europen (and American) call ...
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1answer
1k views

Early exercise of American options

I know this question is considered basic and has been asked millions of times, but I have done my research and there are some points that I just can't understand. For an American call, many ...
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1answer
100 views

Do we need to derive the PDE for the option price when applying Least Squares Monte Carlo?

I want to price an American call option based on an underlying that follows a jump-diffusion process with an inhomogeneous jump frequency function. My mathematical skills are not sufficient to derive ...
2
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1answer
53 views

Pricing Secured Barrier Call 2

EDIT: OK, I understand the reasoning for the initial answer now; however, I don't understand why we would need the digital call with a strike of 33 in this question. Is it just there to serve as a red ...
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0answers
71 views

The last step of the Longstaff-Schwartz method

I'm reading An analysis of the Longstaff-Schwartz algorithm for American option pricing, by Clement, Lamberton and Protter. They define the stopping times (top of page 4) $$ \tau_j^{[m]} = \begin{...
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2answers
74 views

Importance of full value functions for option pricing

Suppose the value of an option is given by $v(s_0)$ where $s_0$ is the current price of the underlying asset and $v:\mathbb{R}_+\to\mathbb{R}_+$. It seems that the literature is mostly focused on ...
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1answer
180 views

Quantlib: AmericanOption implied volatility / root not bracketed

When I apply the americanoptionimpliedvolatility function in the following format: ...
2
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1answer
492 views

Issue Using QuantLib and Python to Calculate Price and Greeks for American Option With Discrete Dividends

I am having trouble using QuantLib with Python to calculate American options with discrete dividends. I am using Anaconda, Spyder, Python 3.6, and the most recent version of QuantLib. I created ...
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1answer
79 views

Binomial Option Valuation Paul Wilmott

I recently purchased Paul Wilmott's Quant Finance FAQ book. In the book he states that the binomial option valuation method is 'rubbish'. Can anyone enlighten me as to what method he recommends for ...
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0answers
51 views

Problem in understanding how to apply Dynamic Programming applied to a Stock Option

I am trying to follow an example in which dynamic programming (DP) is applied to a stock option. I'm familiar with option theory but I'm new to DP. The original exposition can be found on page 6 here: ...
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0answers
28 views

Option style with grant date

The following option exercise style is somewhere between American and European: There is a fixed grant date $N_1$ at which you determine at which date $N_2>N_1$ the option will be exercised. So ...
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0answers
218 views

Brennan-Schwartz algorithm for pricing American options

I'm reading Pricing American Options using LU decomposition by Ikonen and Toivanen (IT). They reference The valuation of American put options by Brennan and Schwartz, and cast it as method that uses ...
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1answer
93 views

Why is accuracy important in pricing American Options?

I see a lot of academic papers talking about accuracy in pricing American Options (and finding analytic solutions). Why is there so much interest in this topic? Isn't the option price set by the ...
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1answer
121 views

Valuing an option when we have a view on future price of underlying

I have a model that predicts the future price of a stock, and would like to incorporate this information to value the option. Lets take an example. AAPL stock is trading at 151.89 US dollars today (...
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1answer
108 views

Intuitively understand boundaries of American Call and Put

Denote American Call/Put $C_{am}/P_{am},$ European Call/Put $C_v/P_v,$ with constant risk-free interest rate $r,$ dividend yield rate $D,$ strike $K,$ maturity $T.$ 1.We have the well know ...