Questions tagged [american-options]

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

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Is it possible to have only one volatility surface for american options (that fits both calls and puts)?

Put-Call Parity does not hold for american options. Hence, I don't see how it would be possible to have one surface that would encompass both calls and puts. For example: Let pick a call lying in the ...
Rodrigo's user avatar
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30 votes
11 answers
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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 ...
dplanet's user avatar
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8 votes
2 answers
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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 ...
Benoit Alessis's user avatar
6 votes
2 answers
1k 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 ...
Elekko's user avatar
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3 votes
1 answer
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How far the spot price is likely to go from the current level in three months if its volatility is 15.7%

On Page 24 of N. Taleb's "Dynamic Hedging" the author gives the following example Example: Assume that an asset trades at \$100, with interest rates at 6% (annualized) and volatility at 15.7%. ...
zer0hedge's user avatar
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11 votes
3 answers
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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 ...
Lost1's user avatar
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8 votes
1 answer
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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 ...
fmc100's user avatar
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2 answers
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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 ...
DeepRed's user avatar
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6 votes
3 answers
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?
Hans's user avatar
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5 votes
0 answers
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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). ...
Dimitri Vulis's user avatar
5 votes
2 answers
12k 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 ...
Yilie Ma's user avatar
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4 votes
4 answers
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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 ...
Prakhar Mehrotra's user avatar
4 votes
2 answers
855 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 ...
Lost1's user avatar
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8 votes
1 answer
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Implied vol and model calibration for an american option on a dividend paying stock - is there a market standard pricing model?

In terms of calibrating a pricing model to observed prices for American options on a dividend paying stock, is there a standard way of doing this in practice? My initial thought was to use CRR ...
AShortSqueeze's user avatar
6 votes
1 answer
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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-...
Jared's user avatar
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1 answer
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Why aren't american put options martingales?

I don't understand what's wrong in the following argument. Assume that we have a no-arbitrage market where the following products are traded: a risky asset $S$, a risk-free bond $B$, an American put ...
chalk's user avatar
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5 votes
1 answer
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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 ...
Hans's user avatar
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3 votes
0 answers
574 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 ...
10uss's user avatar
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3 votes
2 answers
2k 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 ...
galaxyan's user avatar
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3 votes
1 answer
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Early Exercise of American Options on dividend-stock

I am reading the chapter 15 of Options, futures, and other derivatives by John Hull. Specifically, 15.12 Dividends-American Call Options. I am stuck while proving the fact that exercising an American ...
Turtle203's user avatar
3 votes
1 answer
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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 ...
quantfin_enthusiast's user avatar
2 votes
1 answer
321 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 ...
Bananach's user avatar
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2 votes
1 answer
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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 ...
Cettt's user avatar
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2 votes
1 answer
294 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?
vedant bajaj's user avatar
2 votes
0 answers
533 views

American Swaption Pricing with PDE discretization

So I am still trying to price an american swaption. (MC approach here: American Swaption Pricing with Monte-Carlo method) I've found in Paul Wilmott, The mathematics of financial derivatives, a PDE ...
Lucas Morin's user avatar
2 votes
0 answers
510 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 ...
user38310's user avatar
1 vote
0 answers
528 views

Constructing a hedging strategy for an American option

Question: Consider the following model, where $r=0$, and a dividend of 1 unit of currency is paid at time 1.5. $$ \begin{array}{|c|c|c|c|} \hline & S(0,\omega) & S(1,\omega)^* & S(2,\...
veiph's user avatar
  • 11
1 vote
0 answers
237 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 ...
John Doe's user avatar
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0 votes
0 answers
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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 ...
Elon's user avatar
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1 answer
189 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 ...
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