# Questions tagged [american-options]

An option that may be exercised at any time before the expiration date.

307 questions
Filter by
Sorted by
Tagged with
234 views

### Far OTM calculation issue on Bjerksund-Stensland

Has anyone come across and fixed calculation issues on boundaries using Bjerksund-Stensland 2002 (Hull, Haug or Rouah implementations) ? Thanks in advance
98 views

112 views

### implied-information in american option

I have recently been researching European options versus American options implied information. For European options, an overview article is Christoffersen(2012). But for American options, I only found ...
111 views

### How to price lookback american option when its payment is distributed during its life

I would like to price a floating strike american lookback with a particular feature: I don't want to charge upfront the client, rather I would like to insert a "running fee", some sort of a dividend. ...
192 views

### Is this an optimal stopping problem?

I am trying to work out how to approach a machine learning problem of 'learning' an optimal liquidation time/threshold, under some conditions, from historic data. The idea is a trader armed with this ...
159 views

### Convergence rate of Bermudan to American option

When trying to value an American option we often use grid-based methods (e.g. Monte Carlo in combination with Longstaff Schwartz; or Finite Difference Methods). As such, we are in fact estimating the ...
298 views

### Delta-hedge experiment of American Put option

I am trying to run a delta-hedge experiment for an American Put option but there's a (systematic) hedge error which I cannot seem to understand or fix. My implementation is found in the bottom of this ...
90 views

### Implied Volatility Discrepancy in American Options - Mathematical Reasoning?

I've been analyzing Tesla stock American options data and have observed an interesting pattern that I'd appreciate some help understanding. For this analysis, I obtained the Implied Volatilities (IVs) ...
1 vote
70 views

### Optimal exercise time in Binomial model

Let (B, S) a multi period binomial model that is arbitrage free. I would like to prove that the unique optimal exercise time for an American call option is the maturity time T. My idea is to prove ...
66 views

### LSMC for Out of The Money paths

In the Longstaff & Schawartz article they condition on using In-The-Money (ITM) paths only for the regression. The reason for this is to obtain more accurate results and also reduce the ...
169 views

### Is American put Gamma always greater than the European one in the non-early-exercise domain?

Consider a pair of American and European puts with the same specifications except the former has the continuous early exercise right. Has anyone plotted the Gamma's of both as functions of the ...
129 views

### Pathwise sensitivities of American options - Derivative of the American payoff function

How can I compute the derivative of the payoff function for an American put option? In the paper "Smoking adjoints: fast Monte Carlo Greeks" by Giles and Glasserman (2006) they compare two ...
1 vote
456 views

### Under put call parity shouldnt the implied volatility for call and put for same strike and maturity be the same?

If all of the other inputs into black scholes (divs/rates/time to maturity/strick/current price/etc) are all the same between two pairs of calls/put contracts on the same security, shouldn't the ...
1 vote
329 views

### Monte Carlo American Options Discrete Dividends

Built some tree methods to price american options with discrete dividends. But I have no way to really verify my work. Questions below: Does it make sense to build a Monte Carlo pricer to use as a ...
122 views

### Continuation value in Longstaff-Schwartz: Why the expected value?

In the paper by Longstaff and Schwartz on American option pricing, the continuation value at time $t_k$ is given by: \begin{align} F(\omega;t_k) = \mathbb{E}_Q\Big[\sum_{j=k+1}^Kexp\Big(-\int_{t_k}^{...
122 views

### American option pricing formulation

Assuming the usual setup of: $\left(\Omega, \mathcal{S}, \mathbb{P}\right)$ our probability space endowed with a filtration $\mathbb{F}=\left(\mathcal{F}_t\right)_{t\in[0,T]}$, $T>0$ denoting the ...
1 vote
101 views

### Longstaff-Schwarz LS Monte Carlo - which approach is correct? [closed]

I'm trying to understand Least-Square Monte Carlo approach for pricing american options. I'm familiar with Tsitsiklis and van Roy (2001) approach where we are going backwards with: $V_T = h(S_T)$, ...
266 views

### Comparison of the American and European call deltas

Suppose the interest rate is zero. A stock with price $S(t)$ at time $t$ pays only one dividend at time $t_1$ such that $S(s_+)=S(t_1^-)q$ where $q\in[0,1]$ is a constant. Consider a European call and ...
110 views

### If American Options always have positive time value, how can it be optimal to exercise an American Put early? [duplicate]

r > 0. I understand that money today is worth more than money tomorrow. So if volatility is 0, it's better to take the money today. But I don't understand how to square away the following: Time ...
77 views

### How to improve fit in American options vol surface?

I am trying to model the volatility surface of index etfs (spy, iwm and qqq). I am using the CRR model with discrete dividends and the spot model. I find that for some cases there is a noticeable ...
31 views

### How to price an american put option on a dividend-paying stock? [duplicate]

There is no Black Scholes formula for the value of an American put option on dividend paying stock eithe has been produced ? Should I use the binomial model ?
36 views

### Properties of the American derivative security price process

$$\newcommand{\cbkt}[1]{\left\{{#1}\right\}} \newcommand{\rbkt}[1]{\left({#1}\right)} \newcommand{\sqbkt}[1]{\left[{#1}\right]}$$ Shreve volume I, defines an American derivative security as follows: ...
1 vote
144 views

### Put price characterisation

I am reading Shreve's Stochastic Calculus for Finance II: Continuous-Time Models. I am trying to understand the below two concepts: Topic 8.3.3 Analytical Characterization of the Put price on Page ...
346 views

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} \... 1 vote 0 answers 100 views ### Black-Scholes PDE for American options (inequality) I am currently working on American options. I saw that we can derive a PDE for American style options in the same way as with BS for European options. In a textbook, I found that the PDE leads to an ... 0 votes 0 answers 63 views ### Using the SABR Model to Calibrate the Implied Volatility Smile/Surface of an American Option If I already know the implied volatility smile/surface of an American option, can I directly use the SABR model to calibrate the smile/surface, or do I need to make certain adjustments first? 0 votes 3 answers 261 views ### Are "American" option strategies traded OTC? Is there such a thing as an American butterfly spread? For a European butterfly spread simply buying 1 put with strike price X+a, 1 put with strike price X-a and shorting 2 calls with strike price X, ... 0 votes 0 answers 61 views ### Time steps in CRR Binomial Option Pricing for American Options how do you determine the time steps required as inputs to the Cox Rubinstein Binomial Option Pricing model when trying to determine the fair price of an American option? Most textbooks and literature ... 1 vote 0 answers 78 views ### How can I derive the price of american options given the european options prices? [closed] I have the european volatility surface of a given asset. What is the correct procedure to compute the price of the options with american exercise type? 7 votes 2 answers 920 views ### What's the connection between implied vol curve of SPX and SPY? I think there should be an obvious connection of the two implied vol curves from the SPX and SPY markets since the underlying of SPX is SP500, while the underlying of SPY is a ETF which tracks sp500 ... 2 votes 1 answer 242 views ### Does the risk neutral pdf that is derived using Litzenberger-Breeden Method correspond to gamma and it's integral correspond to delta? I derived the pdf using the butterfly prices and the curve looks like gamma of an option at every strike. Is that the case or am I missing something to get the pricing of an option? -3 votes 2 answers 243 views ### Why is accuracy important in pricing American Options? [closed] 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 vote 0 answers 34 views ### Exotic options with lookback features [closed] I am trying to value an american call option with a lookback feature. So the holder can choose to exercise either based on a fixed strike (K) or a floating strike equal to 10-day moving average (MA). ... -1 votes 2 answers 896 views ### Bermudan Swaptions [closed] 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 ... 0 votes 0 answers 57 views ### Binomial Tree for CDF I'm tasked with solving an optimal stopping problem relating to stochastic process representing a firms profit namely X_t = X_0 + \mu t + \sigma Wt where X_0, \mu and \sigma are constants. ... 9 votes 1 answer 470 views ### Why were Laguerre polynomials a good choice of basis functions for American Monte Carlo? I am implementing LSMC to price American options based on a custom model. I now need to make a choice of basis functions, so I am looking for the theoretical justification for using Laguerre ... 2 votes 0 answers 87 views ### What are some good books to get started with option theory? [duplicate] Recently graduated in econometrics but starting to realize my knowledge is limited. Any and all tips are welcome! 1 vote 1 answer 107 views ### Significant digits in numerical derivative pricing I am looking for examples for the number of significant digits commonly required to find numerically the price different types of derivatives. For instance, if we have to price an American put option, ... 2 votes 0 answers 95 views ### Perpetual Option Paying Chooser Option A perpetual option solves the ODE$$rSV_S+\frac{1}{2}\sigma^2S^2V_{SS}-rV=0$$The general solution is$$V(S)=aS+bS^{\gamma} where $\gamma=-\frac{2r}{\sigma^2}<0$. For an American put option with ...
120 views

Several resources I saw introduce the notion of bid/ask spread when trying to price options in incomplete market, I don't understand why the notion is introduced since we are interested on the price ...
1k views

### Convexity of an American put option

Is the price of an American put on an underlying without dividend convex with respect to the strike?