Questions tagged [american-options]

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43 views

American put option reference price that is accurate to at least 6 digits?

I need an accurate reference price of an American put option under GBM dynamics ($r > 0$). I can use many numerical methods, but it would take too long to get any more than 3 or 4 digits of ...
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1answer
179 views

Is gamma always positive for American call/put options under Black-Scholes framework?

Most reference I could find only consider European options, but I would like to know whether this also holds for American options in general (with continuous dividend yield and/or discrete dividends)?
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41 views

Finite difference valuation with early exercise

I am implementing a finite difference pricer for American options using local volatility models. The pricing PDE is given by $$ \frac{\partial V(t,S)}{\partial t}+\left(r(t)-q(t)\right)S\frac{\partial ...
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39 views

Relation between volatility and exercise timing of American Options

Hopefully someone can help me with intuition. Suppose that we have a stock whose value evolves per the geometric brownian motion $dX_t=X_t\mu dt+X_t\sigma dW_t$, for $\sigma>0$, $\mu\in\mathbb{R}$ ...
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1answer
81 views

Why do we care about American options?

I have been told most real options are American. However, this isn't really true. Markets are closed at times, there are delays in transactions, or the owner of the option might be sleeping, or just ...
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1answer
90 views

L2 Assumptions of the Longstaff Schwartz method

In page 121 of the original LS Paper they use the fact that the space of functions they are dealing with (payoffs of American options), belong to the $\mathcal L^2$ space. They use this assumption ...
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0answers
35 views

Optimized search for yield-to-worst of a callable bond

Suppose that I need to find the yield-to-worst of a callable bond, and that the option is American (call any time). The bond may have step-up coupons and/or non-constant call price (oprion strike). ...
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73 views

Short-Term Option Contract Worth Same as Long Term Option Contract At Same Strike?

Let's say that I'm analyzing option contracts for ABC Company, which typically trades at lower volumes. While researching ABC Company, I notice that for a given strike price, contracts that expire in ...
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1answer
1k views

Why the focus on American put options in literature?

I've noticed that in the literature, whenever European vanilla options are to be priced, the classical approach is to price a European call. I guess it doesn't matter because we have put-call parity. ...
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1answer
107 views

Is Longstaff-Schwartz best method for Bermudan options?

What is the go-to method for pricing of Bermudan/American options? I've heard the Longstaff-Schwartz method is really popular. Is it better than the other methods generally speaking? If not, which ...
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2answers
60 views

Lower bound for Bermudan Option Price

i have the following question. The price of an Bermudan option is given by \begin{align*} V_{0} = \sup_{\tau \in \mathcal{T}(0,\dots, T)} \mathbb{E}[f_{\tau}(X_{\tau})]. \end{align*} It is ...
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1answer
62 views

Is it possible to use options to increase the yield of a dividend paying stock?

I was wondering if it is possible to use call options (selling call options) to increase the yield of a dividend-paying stock (that I already own) by 1-2 percent per year? What are the cons of this ...
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59 views

American options & Optimal Stopping Time

From Shreve's book (Stochastic Calculus for Finance II), assuming stock dynamic as standard GBM (without any dividends), the discounted American put price process (which is a super-martingale), ...
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0answers
134 views

Pricing American Options by Neural Networks

Has anyone read the paper 'Pricing of High-Dimensional American Options by Neural Networks' by M. Kohler et al. (2010) and tried to program the proposed method in Python? I have been trying that for ...
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0answers
33 views

What is the effect of put call open Interest on price action

how option put call open Interest affects price actions as put sellers feel price when price goes down or call sellers feel pain when price goes up and how this affects price action. ie when price ...
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2answers
128 views

Price American call equal to price European call (non-dividend-paying stock)

Let $\tilde{C}_K(t,T)$ be the value (price) of an American call option at strike $K$ and maturity $T$, and $C_K(t,T)$ the value (price) of a European call option at same parameters. For a non-...
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0answers
49 views

Are radial basis functions popular in least squares monte carlo option pricing?

In a Longstaff-Schwarz setting option on several underlyings can be priced using least squares monte carlo. Using suitable set of basis functions, continuation values can be approximated using ...
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0answers
63 views

Interchange Expectation and Supremum in Snell Envelope/American Options

I had a question about the properties of a snell envelope, $\sup_{t\le\tau\le T} \Bbb E\left(Z_\tau\mid \mathcal F_t\right)$, which came to me while studying American options. I know that in general,...
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1answer
114 views

On pricing american put options

How come we pick the highest between the discounted weighted average (with risk neutral probabilities) and the early exercise value at each node of the binomial tree? I dont understand why, I can ...
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1answer
146 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?
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27 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 $...
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0answers
49 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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0answers
78 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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0answers
68 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
92 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
162 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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0answers
88 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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0answers
96 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 ...
3
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0answers
157 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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0answers
20 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
233 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 ...
2
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1answer
120 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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44 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
137 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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2answers
204 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
95 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 "...
3
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2answers
147 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 ...
4
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1answer
236 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
57 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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0answers
61 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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0answers
360 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
132 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
137 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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124 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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0answers
20 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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0answers
247 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
117 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
65 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
647 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
130 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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