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Questions tagged [american-options]

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34 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 ...
4
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1answer
89 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 ...
3
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1answer
69 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 "...
2
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2answers
73 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 ...
3
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1answer
122 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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0answers
42 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 ...
2
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0answers
25 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} \...
2
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0answers
77 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
94 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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0answers
48 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 ...
6
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92 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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15 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 ...
2
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0answers
63 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 ...
3
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1answer
71 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 ...
1
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1answer
52 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
233 views

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

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
72 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
94 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 ...
4
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1answer
112 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
50 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
80 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
56 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
245 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
78 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
503 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
95 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
162 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 ...
-1
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1answer
215 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
53 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
60 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
89 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
61 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
217 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(...
1
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1answer
161 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
96 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
104 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
114 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. ...
0
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1answer
86 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
99 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
132 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
473 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
60 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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1answer
102 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
52 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 ...
0
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1answer
65 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 ...
0
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1answer
343 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
2k 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
119 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
63 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
93 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{...