Questions tagged [american-options]

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134 views

Using return on equity instead of risk free rate when pricing an equity call option

I am currently a second year university student studying business, so excuse my lack of knowledge regarding the subject. I am currently studying the binomial options pricing model, which involves ...
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2answers
630 views

Why it is not possible to price American perpetual call option using PDE approach?

Using a standard PDE approach to price an American perpetual put option I obtain that the price of such option has the following form: $$ V(S) = A S + B S^{-2r/\sigma^2}. $$ And then I need to find a ...
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1answer
66 views

Are perpetual american options traded on real stock exchanges?

I am looking for any information about perpetual american options from practical point of view? Are they traded on stock exchanges? Do investment banks deal with such products?
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1answer
118 views

Optimal exercise boundary at expiration

According to Kim (1990, p.560) in "The Analytic Valuation of American Options". I understand the first minimum condition where K sets the lower bound of the optimal exercise boundary at expiry, but ...
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0answers
53 views

Did i miss something on the American put option problem?

Maybe this is a stupid question, i dont know, anyhow i recently read this part from an article, Can someone explain the part " American put value function ...and the exercise boundary jointly solve ...
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1answer
69 views

Put price, payoff, how come? [closed]

From Merton (1973) the following boundary condition is valid for an American put. G(S,t:E) >= Max [0,E-S] I dont understand how the Rational put price can be ...
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1answer
428 views

Am Call = Euro Call if r is non-negative and Am Put = Euro Put if r is negative

It can be proven that under non-negative interest rates, it is never optimal to exercise an American call option, such that: We know, if R >= 0, the current price C of a Europen (and American) call ...
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1answer
3k 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 ...
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1answer
128 views

Do we need to derive the PDE for the option price when applying Least Squares Monte Carlo?

I want to price an American call option based on an underlying that follows a jump-diffusion process with an inhomogeneous jump frequency function. My mathematical skills are not sufficient to derive ...
2
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1answer
71 views

Pricing Secured Barrier Call 2

EDIT: OK, I understand the reasoning for the initial answer now; however, I don't understand why we would need the digital call with a strike of 33 in this question. Is it just there to serve as a red ...
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0answers
106 views

The last step of the Longstaff-Schwartz method

I'm reading An analysis of the Longstaff-Schwartz algorithm for American option pricing, by Clement, Lamberton and Protter. They define the stopping times (top of page 4) $$ \tau_j^{[m]} = \begin{...
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2answers
75 views

Importance of full value functions for option pricing

Suppose the value of an option is given by $v(s_0)$ where $s_0$ is the current price of the underlying asset and $v:\mathbb{R}_+\to\mathbb{R}_+$. It seems that the literature is mostly focused on ...
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1answer
339 views

Quantlib: AmericanOption implied volatility / root not bracketed

When I apply the americanoptionimpliedvolatility function in the following format: ...
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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 ...
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1answer
108 views

Binomial Option Valuation Paul Wilmott

I recently purchased Paul Wilmott's Quant Finance FAQ book. In the book he states that the binomial option valuation method is 'rubbish'. Can anyone enlighten me as to what method he recommends for ...
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0answers
30 views

Option style with grant date

The following option exercise style is somewhere between American and European: There is a fixed grant date $N_1$ at which you determine at which date $N_2>N_1$ the option will be exercised. So ...
2
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1answer
415 views

Brennan-Schwartz algorithm for pricing American options

I'm reading Pricing American Options using LU decomposition by Ikonen and Toivanen (IT). They reference The valuation of American put options by Brennan and Schwartz, and cast it as method that uses ...
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1answer
110 views

Why is accuracy important in pricing American Options?

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 ...
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1answer
130 views

Valuing an option when we have a view on future price of underlying

I have a model that predicts the future price of a stock, and would like to incorporate this information to value the option. Lets take an example. AAPL stock is trading at 151.89 US dollars today (...
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1answer
218 views

Intuitively understand boundaries of American Call and Put

Denote American Call/Put $C_{am}/P_{am},$ European Call/Put $C_v/P_v,$ with constant risk-free interest rate $r,$ dividend yield rate $D,$ strike $K,$ maturity $T.$ 1.We have the well know ...
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2answers
246 views

Binomial tree prices the American put

When we use the binomial tree to price the American put, we should compare the discounted value from last nodes and the intrinsic value at each node. But I confuse that, discounted value from last ...
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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 ...
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0answers
53 views

Pricing American Option Using an Exisiting Boundary

I want to price American Option by applying an existing boundary to a set of randomly generated paths. The boundary can be obtained from a binomial method. For example, a call option with one year ...
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1answer
155 views

SPY American option Greeks and Premium

I am trying to replicate Ivolatility.com's option calculator for a client. Here's the example Using standard Black Scholes model, I can replicate the exact calculations if there is no dividend. With ...
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1answer
248 views

Option price in a neutral risk world is the same as in the real world. I can not understand! [closed]

Good evening. I know there are several posts on the subject but unfortunately I can not fully understand this concept and I hope you can help me. To price the option the fundamental assumption ...
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1answer
60 views

Value of American option after exercise

Suppose $V^+(S,t;K)$ is the value of a American option with strike $K$ before the exercise, and $V^-(S,t;K)$ is the value after exercise. Then how to understand the inequality $$V^+(S,t;K)\geq V^-(S,t;...
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1answer
87 views

Benchmark value for American Options under stochastic volatility

Does anyone know any kind of method that produces reasonably well results for American Options under Heston Model setting that could be used as benchmark value? Since right now my goal is to ...
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1answer
115 views

Estimate American-style option delta from similar options

I have a data set which looks something like this, referring to American-style put and call options: ...
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1answer
143 views

Is there any useful links for option pricing (american + asian + european) using R

I'm trying to evaluate option pricing mainly american, asian and european options in order to get a plot to measure option valuation in time. Is there any useful references to do that using R ?
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0answers
370 views

American Vs European Options behavior with fixed strikes and varying expiration

Following is from page 10 of Fengler (2005), "The prices of American calls for the same strikes must be nondecreasing, Merton (1973), and in the absence of dividends, this property translates to ...
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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 ...
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1answer
263 views

Real Options: Calculating the “option to switch use” using binomial lattices

I'm currently looking into calculating the "option to switch use" to determine the benefit of the ability to switch between two technologies at any point in time (american option). This is also called ...
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1answer
110 views

First passage probability in american option pricing

In an article i recently read (The American Put Option and Its Critical Stock Price by David S. Bunch and Herb Johnson link) the authors presented this formula as something very general and as common ...
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1answer
374 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 ...
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1answer
185 views

why we drop the last term in the Barone-Adesi Whaley formula

In this paper Efficient Analytic Approximation of American Option Values in the first several lines of page 306, the author dropped the last term in equation 11, he explained that when $T\to 0$, we ...
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0answers
243 views

Building implied binomial tree with American input options

i want to build an implied volatility binomial tree with American input options, so the setup is the following: 1) We know the market Price P of the American Put $P_{am}(t_i,K)$, where $t_i$ is the ...
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1answer
144 views

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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0answers
29 views

Some confusion on american put pde

Suppose $$L(v) = \dfrac{\partial v}{\partial t} + rS\dfrac{\partial v}{\partial S} + \dfrac{1}{2}\sigma^2S^2$\dfrac{\partial^2 v}{\partial S^2} -rv$$ is Black-Scholes operator. ...
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1answer
167 views

How to solve one-touch American call

I want to solve the one-touch American call at $t = 0$ with level $B,$ maturity $T$ under the following assumption: $$d S= rSd t + \sigma SdW,\quad S_0<B.$$ We have following formula: $$V(S_0,0) = \...
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2answers
331 views

Would a cash-settled American Option ever be optimal to early exercised?

I know that an American call option on a non-dividend paying stock is never optimal to early exercise, but I wonder why would an American option ever even be optimal to early exercise? My rationale ...
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0answers
232 views

Upper and lower bounds of the early exercise boundary for American option

In the article about Exercise boundaries of American options by F.AitSahlia and T.L.Lai the closed-form formulas for lower and upper bounds of the exercise boundaries are given as follows: It ...
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0answers
162 views

Relative Value Trading of American Style Options on Futures, Calcuating hedging ratios?

I am interested in Relative Value Trading of American style options on futures and have not found a whole lot of literature on it. The best resource I have discovered so far is a few pages in Colin ...
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72 views

ODE Solution in Carr's Randomized American Put

In Carr's 1998 paper Randomization and the American Put, he sets up the following ODE for the value of an American put with expiration given by the first jump time of a Poisson process with rate $\...
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1answer
161 views

Terminal Condition for American Put Option

In a recent book I read, the author mentioned the terminal condition $$\mathop {\lim }\limits_{t \to T} V(S,t) = \max \left\{ {X - S,0} \right\}$$  This is intuitive to understand. Then he defines $...
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0answers
279 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,\...
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1answer
108 views

To Collar or not to Collar

I have a conundrum. I have a stock that has had considerable price appreciation over the past year. Well over 100%. I no longer see any factor (or fundamentals) supporting it's current price (in the ...
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1answer
173 views

Finding the True Option Value

Many research papers use differing solution methods to attempt to find the 'true' value of an option whether it be Euro, American, etc. They never mention how they do find the true option value to ...
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1answer
37 views

is there a dependence between an annotation date of stocks dividend payment and the end fiscal year

I know that the fiscal year in USA from 1 October till 30 September. I'd like to know: is whether there a dependence between a declaration date and an end of fiscal year? I think this dependence ...
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2answers
78 views

Question regarding the derivation of American Put option

When we derive the boundary conditions for the American put options, if we let $S_f(t)$ be the optimal exercise boundary, for $S \gt S_f(t)$ we get $$\frac{1}{2}\sigma^2S^2\frac{\partial^2P}{\partial ...
4
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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 ...