Questions tagged [american-options]
The american-options tag has no usage guidance.
304
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American call and put prices, increasing in maturity
Show that American call and put prices are increasing in maturity $T$.
Does this mean I need to show that as $T$ increases than the American call and put prices increase as well? If so, how do I go ...
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Hedging American Derivative
Reading the book by Andrea Pascucci "PDE and Martingale Methods in Option Pricing", pp. 84, I found something that appears inconsistent to me. It concerns the construction of the optimal portfolio for ...
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2
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Analysis of exercising a call option early
Most options traders sell their call options early instead of exercising them, as you would make a bigger profit this way due to being able to salvage some remaining extrinsic value.
For example:
...
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1
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Pricing of American Deriviatives
Reading the book by Andrea Pascucci "PDE and Martingale Method in Option Pricing" I am struggling with a very simple issue. Suppose we want to find the price of an American derivative $X$ in an ...
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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 ...
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1
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Least-Square Monte Carlo in multiple variable
The paper by Longstaff-Schwatz on Least Square Monte Carlo offers very little proof. The only proof they have given assumed the option can only be exercised at two different time point and the price ...
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4
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pricing american calls on non dividend paying stocks
It is never optimal to exercise an american call option early if it is written on a stock that doesn't pay dividends, yet when pricing such an option, using a binomial model, we check whether or not ...
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How can the time value portion of an option be higher than 100%?
Here's a screenshot from InteractiveBrokers TWS for the near-the-money put and call on the ES Dec '15 Future:
The absolute value of the time value, 9.50, makes sense. But why is the percentage value ...
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Jacobian for Newton method for American options by front fixing
In this paper Penalty and front-fixing methods for the numerical solution of American option problems a front fixing method based on Newton is described for an American put option is described. I am ...
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Is it realistic to assume that the current price of a stock takes into account the probability of it going up or down in the future?
I'm currently reading the following lecture notes: http://www1.maths.leeds.ac.uk/~jitse/math2515/lecture04.pdf
On the second page, under the subsection titled "The Risk-Neutral World" it points out ...
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analytic formula for the value of an American put option
It seems to be a foolish question but I can't take my mind off from , Is it true that there is no analytic formula for the value of an American put option on a non-dividend-paying stock (or a divident ...
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How can one value a Bermudan option?
A Bermudan 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 ...
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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}...
user16651
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Boundary conditions of PDE from SV model with stochastic interest rate
The PDE for the American put option price $P(S,\sigma ,r,t)$ is
\begin{align*}
0 =& P_t+P_SS(r-\delta)+P_\sigma a(\sigma)+P_r\alpha (r,t) \\
+& \frac{1}{2}P_{SS}S^2\sigma ^2 + \frac{1}{2}...
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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 ...
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Hedging portfolio and extraction PDE of SV model with stochastic interest rate
How can I extraction this PDE
\begin{align*}
0 =& P_t+P_SS(r-\delta)+P_\sigma a(\sigma)+P_r\alpha (r,t) \\
+& \frac{1}{2}P_{SS}S^2\sigma ^2 + \frac{1}{2}P_{\sigma \sigma}b^2(\sigma)+\frac{...
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Price of an American call option [closed]
I'm working through revision questions at the moment and we are asked to compute the price of an American call option.
Suppose that $dS_t = \sigma S_t dW^*_t, S_0 >0$
Let $0<U<T$ be fixed ...
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Value of European Call equals Value of American Call, Question on Explanation/Proof
I am reading S. Shreve, Stochastic Calculus for Finance, Vol. I. There he proves that American Call Options have the same value as European Call Options. In the proof he uses that for a Call option ...
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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 ...
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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.
...
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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 ...
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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 ...
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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 ...
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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 ...
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Hedging behind the decomposition of american put options
Now I'm reading a paper:"alternative characterizations of american put options" , the authors are Carr,Jarrow,Myneni
http://www.math.nyu.edu/research/carrp/papers/pdf/amerput7.pdf
After theorem 1 (...
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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, ...
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Complicated American style option contract with numerous non-standard features (simultanous exercise, additional premium, etc.)
I want to value the following contract for times $0<t<T$, i.e. determine $V(t,\cdot)$ where $\cdot$ refers to all other dependences (strike, spot, volatility, etc.). The contract is long and ...
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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 ...
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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=...
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Pricing American with floating strike
Consider a American floating strike put option with maturity $T$, written on a non-dividend paying stock $S_t$. The strike of this option at time $t\leq T$ is $Ke^{-r (T-t )}$, where $r$ is the ...
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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 ...
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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 ...
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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 ...
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What is the effect of dividend yield being greater than the risk-free rate to American options pricing?
Even though dividends are discrete, literature often makes the assumption of continuous dividends (mostly in the case of indices but the individual stocks as well).
The dividend yield denoted by q is ...
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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,...
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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.
...
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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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Efficient numerical approaches for pricing American Options with multiple sources of noise
I am looking for efficient numerical approaches for pricing American options when two or more sources of noise are involved (the simplest case coming to mind would be the Heston Model)
Eventhough I ...
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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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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 ...
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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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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 ...
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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 ...
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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?
...
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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 ...
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How are option expiration dates decided?
I looked at the CBOE website and they say the expiration is the Saturday following the third Friday of each month. However, I look up an options chain for Google, for example, and I see three ...
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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 $) and its ...
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Early execise of American Call on Non-Dividend paying stock.
Let us consider an American call option with strike price K and the time to maturity be T. Assume that the underlying stock does not pay any dividend. Let the price of this call option is C$^a$ today ...
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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 ...
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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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