# Tagged Questions

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### Finding optimal drift, importance sampling, least square monte carlo

I am working with Importance sampling for Least Squared monte carlo and have now problems understanding the implementation of the Robbins-Monro algorithm for finding the optimal drift for finding ...
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### How to calculate implied borrow rates from option chain information?

I am given information about a ticker with following options data: stock price, date, expiration date, strike price, call / put indicator, style (American or European), ask price, bid price, mean ...
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### compute volatility and greeks of american option on futures using matlab toolbox

I have learned some knowledges on option pricing by myself at a very beginer's level. I'm using matlab R2009b finacial derivative toolbox, I found option pricing functions for american options on ...
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### Importance Sampling for Least Square Monte Carlo

I am currently trying to implement and model an Importance Sampling estimator for Longstaff and Schwartz algorithm for pricing American put options. It is used such that more paths are in-the-money ...
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### American option - Upper bound

I have computed a lower bound for an american option through longstaff and schwartz's algorithm. Now I have to compute the upper bound as andersen and broadie does in their article. Can anybody help ...
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### Is there any literature on a closed-form/analytical solution for American option prices with use of Chaos Theory?

I found the following paper which uses homotopy analysis for a closed-form solution. Does it have direct/apparent connections with chaos theory? http://bfi.cl/assets/zhao-wong-2006---a-closed-form-...
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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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### Equivalent call option to the underlying stock

Would there be any benefit to an investor to purchase an American Call option on a single share with no expiration date and a strike price of 0 as opposed to purchasing the underlying zero dividend ...
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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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### A paradox about the American Put option price

Suppose a put option on a stock $S(t)$ following a Geometric Brownian motion is given, with strike $K$ and maturity $T$. Let us denote its price at time $t$ by $p(t,S(t))$. Now, by no-arbitrage ...
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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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### 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 ...
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### Who Uses American Options?

...in other words, why would a person want to have the right to exercise an option early? What advantage does that really give you? Are Euro-style options not good enough for some people? Who are ...
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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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### Yahoo Finance Implied Volatility Calculation

On 5/16/16 AXP stock closed with a price of 64.07. Yahoo Finance reports an implied volatility of 20.58% for this out of the money call option: ...
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### American call early exercise, considering a portfolio

Im aware there are lots of questions about this, but I am interested in a particular method of showing why an american call (with no dividends) should not exercised early. Here is the text I'm ...
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### Andersen Broadie American/Bermudan Put

I'm trying to implement Andersen and Broadie's dual method for an upper bound (here) of a regular American Put. I understand the process to compute it, but I have a conceptual issue : everything ...
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### Perpetual American Put Supermartingale property

Discounted price process of an american put (perpetual) has a $dt$ part in it, which is negative if the price at time $t$ is less than the optimal exercise price. This is the only thing that drags the ...
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### 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-...
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### Isn't Black's approximation for American options inconsistent?

I have came across a formula suggested by Fisher Black (Fact and fantasy in the use of options, FAJ, Julyâ€“August 1975, pp.36) for approximating the price of an American call written on a dividend-...
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### Perpetual American options

Formulate and solve the free boundary problem for the perpetual American options with the following payoffs. a.) $(S - K)_{+} + a$ where $a > 0$ b.) $(K - S)_{+} + a$ where $a > 0$ ...
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### Two-period binomial model for American option

Consider a two-period binomial model for a risk asset with each period equal to a year and take $S_0 = 1$, $u = 1.5$, and $l = 0.6$. The interest rate for both periods is $R = .1$. a.) Price an ...
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### 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 ...
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### 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 ...
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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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### 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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### 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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### 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 ...
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 ...