Black-Scholes is a mathematical model used for pricing options.

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Is vega of Black-Scholes European type option always positive?

We assume we work in the risk-neural measure with a stock which pays no dividend and a continuous discount rate. For PUT and CALL only: can someone please clarify if what I said is correct? The ...
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1answer
263 views

Black-Scholes fastest computation method

What is the fastest way to numerically compute Black-Scholes-Merton option prices? I'm trying to find fastest and still precise method. Currently I'm using numerical approximation of Normal cdf with ...
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139 views

Time-zero price of two specific contingent claims

I am unsure how to start with the following problem. I have two contingent claims where contingent claim (1) pays $\int_0^T S_u du$ and contingent claim (2) pays $(\log S_T)^2$ at time $T$ Now I ...
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1k views

price of a “Cash-or-nothing binary call option”

I'm stuck with one homework problem here: Assume there is a geometric Brownian motion \begin{equation} dS_t=\mu S_t dt + \sigma S_t dW_t \end{equation} Assume the stock pays dividend, with the ...
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1answer
149 views

Trouble arriving at Black-Scholes Formula

I am attempting to arrive at the Black-Scholes formula for my own understanding. I can accept one can use the risk-free distribution & rate, so I am attempting to use the distrution to arrive at ...
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203 views

options pricing using vwap

This is a question about why options prices do not take volume into account. The popular option valuation formula "black-scholes" certainly does not account for this and I don't suggest that it does. ...
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326 views

Basic question about Black Scholes derivation

In the derivation of the Black Scholes equation, the value of the portfolio at time $t$ is given by $$P_t = -D_t + \frac{{\partial D_t}}{{\partial S_t}}S_t $$ where $P_t$ is the value of the ...
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128 views

Lookback option explicit formula using Black Scholes

I would like to compute the time-0-price for a lookback option using Black Scholes formula, the explicit formula is given by ...
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1answer
212 views

what's the relationship between forecasted stock volatility and implied volatility?(option)

what's the relationship between forecasted stock volatility and implied volatility? I know that implied volatility is the volatility calculated by BS formula, is there any relationship between implied ...
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126 views

Black-Scholes PDE to heat equation, nonconstant coefficients

Can someone provide me with details or a reference on how to transform the Black-Scholes PDE with nonconstant coefficients (i.e. $r=r\left(S,t\right)$, $\sigma=\sigma\left(S,t\right)$) to the heat ...
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1answer
409 views

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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2answers
278 views

Black-Scholes: Why the focus on volatility?

We know Black-Scholes is an imperfect model for options pricing. Why is so much of the analysis of its defects focused on implied volatility? The fact that IV varies for the same stock at the same ...
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399 views

Trading days or calendar days for Black-Scholes parameters?

Black-Scholes requires volatility estimated in trading days. How does this affect other parameters? Specifically, should the time-to-expiration also be in trading days? And how does this affect the ...
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1answer
151 views

Black-Scholes derivation assumption contradiction

In many books and derivations of the Black-Scholes PDE one sees that $$\Pi=V-\Delta F \Rightarrow d\Pi=dV-\Delta dF$$ which implicitly assumes that $d\Delta=0$. Somewhere down the road one then ...
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2answers
102 views

Lower bound of ITM Calls when computing Implied Volatility

Assuming the Black Scholes model and pricing formula of a European call option. Then, if the call is ITM, i.e. if $ln(\frac{S}{K})>0$, the $d_1$-term will go towards infinity as $\sigma$ goes to ...
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1answer
230 views

Black (1976) model: relationship between spot and forward prices

Does the Black (1976) model require the existence of the relation $F(t,T)=S(t)e^{r(T−t)}$? I studied the derivation of the Black-Scholes formula. However, although I know the Black formula, I've ...
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1answer
219 views

What are $d_1$ and $d_2$ for Laplace?

What are the formulae for d1 & d2 using a Laplace distribution?
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1answer
208 views

What is the difference between the methods (listed in content) in pricing convertible bond?

To price the convertible bond, one of the models is the bond plus equity option method. That is, the value of convertible bonds is evaluated by finding the value of the straight bond and the value of ...
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1answer
212 views

Formula for variance of European call/put in Black Scholes

I have a quite basic question, but I can't find a reference with it. Recall that we can use the Black-Scholes formula to price a European call or put for a market consisting when: the underlying ...
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37 views

Black Scholes vs Binomial Model

I'm trying to confirm my understanding of the 2 models. It is my understanding that the black-scholes is a special case of a binomial model with infinite steps. Does this mean that if I were to start ...
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27 views

At-the-money Call Spread approximation

In a trading manual I got during a course, the value of the ATM Call-Spread is approximated by $CS_{ATM}=\frac{1}{2}StrD+(F-m)\times\Delta CS$ The lecturer skipped the part where he derived this ...
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1answer
66 views

American Swaption Pricing with Monte-Carlo method

I want to price an American swaption but I am not sure about what I am doing. Tree methods and PDE discretization seem difficult to adapt to a swaption. I am trying a Monte-Carlo approach. (in ...
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53 views

Calculating the error of a Trinomial Model

I've been trying to find a formula to obtain the maximum relative error a trinomial model with n timesteps will incur given all other inputs as compared to the standard BSM model. I'm concerned mostly ...
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Black-Scholes in Delphi [closed]

when trying to implement the Black-Scholes formula in Delphi, I've found this: http://www.espenhaug.com/black_scholes.html I've checked the results against option-price.com and found they are ...
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76 views

Changes to option valuation for dollar-pegged underlying

In Russia, options on futures on the RTS index are priced in points instead of currency, with points being directly related to the value of the US dollar such that, for example, if the dollar rises, ...
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Why do some people claim the delta of an ATM call option is 0.5?

I am looking for a mathematical proof in terms of differentiating the BS equation to calculate Delta and then prove it that ATM delta is equal to 0.5. I have seen many books quoting delta of ATM call ...
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100 views

Calculate volatility from call option price

Given call option price, what is the simplest formula to get the volatility value ? Test Data: ...
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361 views

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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403 views

Black Scholes Formula for Collar Option

I am wondering if there exists a Black Scholes pricing formula for a collar option?
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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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210 views

Price of a down-and-out call in terms of European call

If $EC(S_0, K, \sigma, r, T)$ represents the price of a European call option with strike $K$, expiry $T$, initial price $S_0$, volatility $\sigma$ and where the constant interest rate is $r$, then I ...
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1answer
183 views

Testing Black Scholes Analytical Options Pricer

I've written some code to calculate European option prices using the Black-Scholes analytical method. Can somebody recommend a good way to test that code? I have looked at option pricers online like ...
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1answer
75 views

what is the vol in the BS formula?

I need to compute the delta of an option for which I know a) the time to maturity, b) the price of the option, c) the price of the underlying asset. what is the formula to get this delta It seems ...
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109 views

How does Vega of a call/put behave under the Black-Scholes model?

I have two questions. I would prefer a reference if possible. Is the value of vega bounded for $\sigma\in [0,\infty)$? (I assume so, I imagine it goes to 0 as $\sigma$ go to infinity.) Are there any ...
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114 views

Error message in calculation Implied Volatility

I am unsuccessfully trying to find the Implied Volatilities for the SPX on a given date using information of the CBOE, as well as Open Interest, but as I run the code I am getting and error message ...
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156 views

Arbirtage free price process question in Bjork's Arbitrage Theory in Continuous Time

I am currently working through questions in Bjork's Arbitrage Theory in Continuous Time. However, I am unable to solve the following question, 7.2 in the book. A solution would be greatly appreciated. ...
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1answer
198 views

How to prove price of Asian option under geometric averaging is cheaper than a European call?

This was an exam question at Cambridge University. Let $S_t = S_0\exp(\sigma W_t + (r-\dfrac{1}{2}\sigma^2)$ and a bank account returns a continuously-compounded rate of interest $r$. Consider the ...
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195 views

Black 76 for Options on Interest Rate Futures

This is my first time using Black76 to value options on IR futures and I have a question on $F$ and $K$. I understand the price for an IR future is usually quoted as $100 - r$. Do I use this price ...
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1answer
581 views

What precision do I need to calculate implied volatility?

I'm developing a software to calculate the implied volatility of an option using the Black & Scholes formula and a trial-and-error method. The implied volatility values I get are correct, but I ...
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1k views

Black Scholes and Monte Carlo implementations in Java [duplicate]

Possible Duplicate: Is there an all Java options-pricing library (preferably open source) besides jquantlib? Can anyone recommend a library with an implementation of Black Scholes and Monte ...
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125 views

Black Scholes well coded Python

I have some trouble with the following code. Some jump and a decentered path are present but it's not the case, normally for Black Scholes diffusion ! Is anyone see a problem in my code ? ...
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416 views

Question about Merton model to estimate default probability and recovery rate of the company

I recently come across Merton's model to estimate the default probability and recovery rate of the company. Here is the inputs ...
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138 views

Pricing a Power Contract derivative security

I'm trying to price a "power contract" and would appreciate guidance on the next step. The payoff at time $T$ is $(S(T)/K)^\alpha$, where $K > 0$, $\alpha \in \mathbb{N}$, $T > 0$. $S$ is ...
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127 views

Am I reading this correctly? probability way too small with BS model

For a stock trading at $27, $28 strike, 0% interest, 15% annual vol, and one day until expiration there is about a 1 in 17000 chance of it being exercised? $d_2 = ...
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354 views

Why the implied volatilities calculated are so different

I Calculated facebook option(expired in 12/4/13) Implied Volatility with the Bisection Method. The program will be attached at the end. The results for different strike prices are so different: ...
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402 views

Drawbacks of Black-Scholes option pricing model

Will highly appreciate if anybody can provide logical financial proof why the Black-Scholes option pricing model overestimates the value for long-term options as described in this paper "Warren ...
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3answers
195 views

Black model - volatility estimation

In the Black (1976) model: We should use the settlement prices of the underlying futures contract in order to estimate the volatility, right? Or can we also use the spot prices? Because the ...
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1answer
155 views

volatility Table and BS formula

assume I have implied FX volatility Delta-Term table from broker. I have time noticed as 2M, 3M. what do I have to put into BS formula, is it 2/12 or "count the business days"/"daycount basis"? I am ...
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283 views

Question about option theta

I have a question about a option theta. When I evaluate the option theta of near expiry put option using Black-Scholes formula given the data as follow: Index Level = 20,500 Strike Price = 20,000 ...
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537 views

How to calculate return rates with negative prices?

I'm dealing with electricity options and I'm considering the possibilty of negative prices. I want two estimate the historic volatility. However, an arithmetic mean doesn't feel appropriate and ...