Questions tagged [american-options]
The american-options tag has no usage guidance.
28
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28
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11
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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 ...
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7
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 ...
6
votes
2
answers
1k
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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 ...
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3
votes
2
answers
477
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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 ...
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2
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%. ...
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11
votes
3
answers
1k
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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 ...
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8
votes
1
answer
4k
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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 ...
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7
votes
2
answers
870
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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 ...
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5
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3
answers
1k
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Convexity of an American put option
Is the price of an American put on an underlying without dividend convex with respect to the strike?
- 2,651
5
votes
0
answers
143
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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). ...
- 11.3k
4
votes
2
answers
787
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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 ...
- 987
4
votes
4
answers
14k
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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 ...
- 143
7
votes
1
answer
1k
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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 ...
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6
votes
1
answer
654
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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 ...
- 61
5
votes
1
answer
243
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 ...
- 2,651
5
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-...
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3
votes
0
answers
535
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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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3
votes
1
answer
4k
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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 ...
3
votes
1
answer
297
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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 ...
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votes
2
answers
2k
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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 ...
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2
votes
0
answers
511
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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 ...
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2
votes
1
answer
293
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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 ...
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2
votes
0
answers
459
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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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2
votes
1
answer
1k
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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 ...
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1
vote
0
answers
507
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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,\...
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vote
0
answers
209
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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 ...
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votes
0
answers
56
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 ...
- 1
0
votes
1
answer
138
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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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