Questions tagged [american-options]

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1answer
939 views
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Constructing Volatility Smile from American Options

My question is about best practices for reconstructing volatility smiles for a fixed tenor from American option data. For simplicity/liquidity, I am currently considering options on SPY. I am ...
2
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1answer
415 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 ...
2
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2answers
106 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 ...
2
votes
1answer
98 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} \...
3
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1answer
167 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 ...
2
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1answer
72 views

Do Perpetual American Options have closed form functions to compute the Greeks?

I was wondering if there were analytical formulas to compute delta or gamma for perpetual American options?
0
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0answers
22 views

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 $...
1
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0answers
34 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 ...
1
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0answers
54 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 ...
3
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0answers
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:...
1
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1answer
65 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:...
1
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1answer
104 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?
1
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0answers
67 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 ...
2
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0answers
76 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 ...
2
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0answers
63 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 ...
-2
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2answers
395 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
votes
3answers
353 views

A paradox about the American Put option price

Suppose a put option on a stock $S(t)$ following a Geometric Brownian motion is given, with strike $K$ and maturity $T$. Let us denote its price at time $t$ by $p(t,S(t))$. Now, by no-arbitrage ...
0
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0answers
17 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 ...
4
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1answer
119 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 ...
1
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1answer
92 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 ...
1
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4answers
277 views

How to calculate return on investment for an adjustment to a complex options position?

Say I currently hold a set of options positions with the same symbol/expiry that collectively have a net present value based on the estimated value at expiration of +10. I could also liquidate the ...
2
votes
1answer
82 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 ...
0
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0answers
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, ...
0
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1answer
74 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 ...
2
votes
1answer
90 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 "...
1
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0answers
47 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
34 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
132 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 $$...
0
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2answers
114 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 ...
0
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0answers
79 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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0answers
111 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,...
2
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1answer
3k 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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0answers
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 ...
2
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0answers
116 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
79 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
58 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 ...
0
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1answer
102 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
votes
2answers
374 views

Foresight bias in least square monte carlo

Foresight bias means we tend to over estimate the American option value. This we observe in other areas of statistics - e.g. in sample test almost always gives better prediction than out of sample ...
0
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1answer
172 views

Least-Square Monte Carlo in multiple variable

The paper by Longstaff-Schwatz on Least Square Monte Carlo offers very little proof. The only proof they have given assumed the option can only be exercised at two different time point and the price ...
2
votes
1answer
99 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(...
7
votes
1answer
269 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 ...
4
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1answer
215 views

Pricing the European counterpart from American Options

I have American option prices for SPY and need to calculate the equivalent European option price to use in further calculations. What does it (formally) mean to price the equivalent European option ...
4
votes
1answer
123 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 ...
1
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0answers
58 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 ...
1
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1answer
101 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 ...
1
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0answers
70 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 ...
1
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1answer
134 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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1answer
884 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 ...
-2
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1answer
110 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 ...
-1
votes
1answer
253 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 ...