Questions tagged [american-options]

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20
votes
9answers
47k views

Exercising an American call option early

I have seen the rationale behind why it is never optimal to exercise an American call option early, but have a question about it. If the option strike price is $E=\$20$ and it expires at $T=1yr$, if ...
11
votes
2answers
4k views

Implied Volatility from American options (binomial)

I am trying to get the implied volatility from options on commodity futures and I know it's possible to get it from the binomial american options (on an non-dividend paying stock). I believe it is ...
10
votes
3answers
534 views

American Call: when it's European?

It is a rather well-spread fact that in Black-Scholes (BS) model for a stock with no dividends that follows Geometric Brownian Motion (GBM), the price of American call coincides with that of its ...
10
votes
3answers
790 views

When is it rational to exercise a bond option early?

Consider american options on interest rate futures such as the 10-year treasury note. When is early exercise optimal?
9
votes
3answers
673 views

How to choose a risk-neutral measure when the market is incomplete?

I am more of a probabilist than a financial mathematician. I am currently working on the features of American put options under a particular stochastic volatility model. Like most stochastic ...
8
votes
1answer
4k views

Longstaff-Schwartz (Least Squares Monte Carlo) applied to American Options

I'm working on an implementation in R of Longstaff & Schwartz method from the this 2001 article. I've managed to build code that replicates their prices in table 1 (p. 127), but only for the ones ...
8
votes
1answer
173 views

Does price of american (put) option exhibit smooth pasting in time direction under B-S model?

Let us consider the BS model and let $f(s,t)$ denote the price of an American put option with $t$ to expiry, then it is known the solution of the optimal stopping (when it is risk neutral) related to ...
8
votes
0answers
865 views
+50

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 ...
8
votes
0answers
244 views

American Swaption Heding with Malliavin Calculus

Hedging American Swaption Hello, I priced an American swaption using Black model with swap rates diffusion to find the european (call) price at t. $$ C_t = (\delta \sum_{j=n+1}^{M+1} Z_t^{T_j})[R(t,...
7
votes
2answers
3k views

The Upper Bound of an American Put Option

I have just read the following paragraph (in bold) and have a question on the upper bound of an american put option: http://www.sharemarketschool.com/option-valuation-upper-and-lower-bounds-part-...
7
votes
2answers
687 views

Least Square Monte Carlo - american Call Option

An American Call Option on an non dividend paying stock has the same value as a european one. I tired to compare the results given by the LSM with the results given by the B&S formular. It seems ...
7
votes
1answer
268 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 ...
7
votes
1answer
585 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 ...
7
votes
0answers
122 views

recent developments in American options?

I have read the paper written by Egloff (2005) using machine learning techniques to solve the optimal stopping problem. Is there any development in pricing American options during 2005-2016? (based ...
7
votes
0answers
307 views

Pricing an American call under the CGMY model

I am pricing an American call under the CGMY model ($0 < Y < 1$) with strike $K$ at grid point $(x_i,\tau_j)$ where $x_i=x_{min}+i\,\Delta x $ for $i=0,1,...N$ and $\Delta x=\frac{x_{max}-x_{min}...
6
votes
1answer
1k views

Modified bisection formula for deriving implied volatility for a dividend paying american option

I am trying to work out the formula for calculating the implied volatility of an american option on a stock paying dividends (discrete payments or annualized yield). On page 171 of Haug The ...
6
votes
1answer
297 views

Upper bound concerning Snell envelope

Consider a non-negative continuous process $X = \left (X_t \right)_ {t\geq 0}$ satisfying $ \mathbb E \left \{ \bar X \right\}< \infty $ (where $ \bar X =\sup _{0\leq t \leq T} X_t $) and its ...
6
votes
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,...
5
votes
3answers
379 views

Can call options be priced with Least-Squares Monte Carlo?

I have been reading about Least-Squares Monte Carlo (using Longstaff & Schwartz algorithm) for option pricing. So far, I have only read examples that uses LSMC for american/bermudan PUT options ...
5
votes
2answers
1k views

American put for negative interest rates

It is often explained, that the rule of thumb for exercising American options is to check when the benefit from the interest rate (sell the stock earlier, get the cash, put in the bank) is higher than ...
5
votes
1answer
294 views

Intuition behind American Option pricing

The price of an American option is given by $$V_n = \max\left(G_n,\frac{pV_{n +1}H^d + qV_{n + 1}H^u}{1 + r}\right)$$ where p, q are the risk neutral probabilities. I have two questions: How can ...
5
votes
2answers
9k views

Value of American Call vs Value of European Call when using implicit finite differences

I calculated values for put options (european and american) using the implicit finite difference method and compared them to black/scholes values. The values for american put options are higher than ...
5
votes
1answer
118 views

Methodology for handling short american options in a back test

Given that an American option can be exercised at any time, how does one handle algorithmically shorting an American option in a back test? I am not sure what the best practice is to simulate the ...
5
votes
0answers
79 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. ...
5
votes
0answers
246 views

LSM American Option pricing with dividends

Under the Longstaff-Schwartz LSM method for an American call, how should I account for a continuous dividend paying stock? I assume that it'll needs to be accounted for when simulating the underlying ...
4
votes
2answers
2k views

American Options relation between greeks

Considering an American option in a Black-Scholes model, is there a relation between Vega and Gamma as it holds in the European case? I am aware an exact relation would be difficult to find. But in ...
4
votes
4answers
11k views

Early execise of American Call on Non-Dividend paying stock.

Let us consider an American call option with strike price K and the time to maturity be T. Assume that the underlying stock does not pay any dividend. Let the price of this call option is C$^a$ today ...
4
votes
2answers
1k views

How to price long dated options most efficiently?

hi question is how to price a long dated option most computationally efficiently? With European, you use Black Shoals (yes assumption constant vol/rates...etc) but it's a simple algebraic formula. ...
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 ...
4
votes
2answers
372 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 ...
4
votes
1answer
673 views

Estimating early exercise boundary for American put

I am trying to estimate the early exercise boundary for an American put option. I can find the put value through the Longstaff-Schwartz LSM method. How do I obtain the early exercise boundary within ...
4
votes
1answer
372 views

Soft American Options

On Page 24-25 of N. Taleb's "Dynamic Hedging" the author talks about "Soft American Options" A soft American option (also called a pseudo-European option) is only subjected to early exercise from ...
4
votes
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
2answers
720 views

Importance Sampling for pricing options with longstaff and schwartz

I have been asking this similar question before. However, I really want to be concrete and get and concrete explanation. I have been reading the paper by Moreni and try to implement the same ...
4
votes
2answers
547 views

Solution for american perpetual put

I have been attempting an exercise in which I have to determine the value of an american perpetual put, $P$ in terms of the asset value $S$. The solution to the exercise says: When $S>S_f$ (the ...
4
votes
1answer
307 views

Literature on Empirical Option Pricing

When I started combing through the literature I was astonished about how little the option pricing models are tested against market data and benchmarks are limited. The main barrier is of course ...
4
votes
2answers
348 views

Machine learning for non optimal behaviour

I was working on the pricing of complex bermudean swaption when I noticed that the exercise is often (very) subobptimal. It seems that the clients are more sensitive to past growth or drop in rates ...
4
votes
1answer
2k views

How can one value a Bermuda option?

A Bermuda option allows early exercise at predefined dates, e.g. at maturity equal to $t_1$, $t_2$, $t_3$,...; hence , would its value be the sum of 3 discounted European options with 1-year ...
4
votes
1answer
752 views

Black-Scholes American Put Option

Here is my question: This is a question about Black-Scholes model, but it may be applicable to more complicated models. Throughout the discussion, the strike price $K$, interest rate $r$ and ...
4
votes
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 ...
4
votes
0answers
2k views

Implied volatility from American options using python

I am currently trying to construct volatility surface from american option prices (using Cox-Ross-Rubinstein tree) in Python 2.7. Below you can find the code I came up with. Any corrections would be ...
4
votes
0answers
250 views

negative transition probabilities in the heston model

I've been trying to implement a bivariate tree for pricing american options with the heston model in R using the paper of Beliaeva and Nawalkha (http://papers.ssrn.com/sol3/papers.cfm?abstract_id=...
3
votes
1answer
2k views

Implied Volatility Surface - log forward moneyness

I'm reading this paper by Fengler (2005) and have came across the below snippet. context: Implied volatiltiy surface plot has 3 dimensions IV, Strike, Time to Maturity. Author replaced Strike with ...
3
votes
1answer
977 views

Understanding early exercise of options - The implicit put in an American call

I am self-studying for an actuarial exam on models for financial economics. I am having a hard time grasping the concept highlighted in red: I was wondering if someone could further elaborate on why ...
3
votes
1answer
1k views

Implied Dividend from American Options (in practice)

I just tried to price the implied dividend for a few active, liquid options markets using current prices and I am not convinced my results are accurate. I am using American options, and using the put-...
3
votes
2answers
1k views

Pricing an american style option on a bond future

what is the good way to pricing american option on bond future? From bonk fixed income securities 3rd by Tuckman, I understand how to pricing European option on bond future, but I still have no clue ...
3
votes
2answers
2k views

Relationship between European, American options volatility

Suppose, if the price of a European option (say a put) can be shown to be monotone in volatility (say for any maturity), does it follow that American options has to be monotone in volatility? ...
3
votes
1answer
1k 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 ...
3
votes
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 ...
3
votes
1answer
542 views

Why future (forward) volatility smile is important to path dependent option?

I was wondering why future volatility smile is important to path dependent option and American type option such as Bermudan swaption. It would be best if someone could provide a reference article as ...