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

learn more… | top users | synonyms (1)

2
votes
2answers
506 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 ...
2
votes
1answer
363 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 ...
2
votes
1answer
224 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 ...
2
votes
1answer
346 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 ...
2
votes
1answer
232 views

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

What are the formulae for d1 & d2 using a Laplace distribution?
2
votes
1answer
102 views

Black-Scholes under stochastic interest rates

I'm trying to implement the Black-Scholes formula to price a call option under stochastic interest rates. Following the book of McLeish (2005), the formula is given by (assuming interest rates are ...
2
votes
1answer
64 views

Black Scholes Model and Dividends

My question can be summarised as such: Consider a portfolio. Say it has a price $\Pi = x$. Portfolio consists of a stock and a sequence of call options underlying on the stock. It has been announced ...
2
votes
1answer
79 views

The source of “Cost of hedging” in the Black Scholes model

I am trying to get some intuition for the fact that a Black-Scholes price for an option is equal to the cost of replicating the option. Say the interest is 0. The option is obviously still worth ...
2
votes
1answer
154 views

Why is the volatility smile important

One thing I can't understand clearly is why there is so much focus on the volatility smile. Given my knowledge of the Black and Scholes model, this is what I get: People use the volatility smile as a ...
2
votes
1answer
1k 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 ...
2
votes
1answer
425 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 ...
2
votes
1answer
560 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 ...
2
votes
2answers
2k 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 ...
2
votes
1answer
22 views

Range options in BS

I know how barrier options are priced in Black-Scholes scheme. I'm wondering if an analytical formula exists also for range (corridor) digital options i.e. options paying only if the price remains ...
2
votes
0answers
49 views

Hedging - calculating option prices using implied volatility surface

To hedge a strategy is it accurate "enough" to price an option using an implied vol curve vs moneyness (strike/spot) assuming sticky delta? The moneyness can be read off the chart, its corresponding ...
2
votes
1answer
235 views

Method for finding a arbitrage opportunity when market price of call is incorrect

The solution of the Black-scholes equation is the price of a European call. And the option price assumes the underlying stock is a geometric Brownian motion with volatility $\sigma_{1}>0$. ...
2
votes
0answers
56 views

In which divisions of banking are the Greeks and Black Scholes equation applied? [closed]

I know that Black Scholes and the Greeks are important in market risk. In what other areas are they used?
2
votes
0answers
53 views

What is the main reasons to use Miltersen & Schartz (1998) model for commodity futures options

versus a standard Generalised Black and Scholes model (if there are any?) I have read the paper but I am not to sure about its practical implications as would people with more experience using this ...
2
votes
0answers
79 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 ...
2
votes
0answers
59 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 ...
2
votes
0answers
157 views

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 ...
2
votes
0answers
80 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, ...
1
vote
1answer
416 views

How to get Geometric Brownian Motion's closed-form solution in Black-Scholes model?

The Black Scholes model assumes the following dynamics for the underlying, well known as the Geometric Brownian Motion: $$dS_t=S_t(\mu dt+\sigma dW_t)$$ Then the solution is given: ...
1
vote
2answers
95 views

Using Black-Scholes to price a geometric average price call

Sorry if this is the wrong exchange for this question. It seems to be the most relevant, anyway. I'm trying to learn and understand the Black-Scholes framework, with a focus on the stochastic ...
1
vote
3answers
165 views

Implied Vol vs. Calibrated Vol

Consider the Black-Scholes model, in which the log stock return over a time period $\Delta t$ is given by $$ \log(S_{i+1}/S_i) = (\mu - \sigma^2/2)\Delta t + \sigma \sqrt{\Delta t} Z_i, \qquad Z_i ...
1
vote
2answers
1k views

Calculate volatility from call option price

Given call option price, what is the simplest formula to get the volatility value ? Test Data: ...
1
vote
2answers
743 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? ...
1
vote
2answers
1k views

Black Scholes Formula for Collar Option

I am wondering if there exists a Black Scholes pricing formula for a collar option?
1
vote
2answers
5k views

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 ...
1
vote
1answer
93 views

Pricing call option

Question: The price of a stock is 100. With equal probabilities, it either goes up to 130 or down to 70. What is the price of a 1 year call option with exercise price 100. Risk free rate is 5%. ...
1
vote
2answers
182 views

Implied Volatility Calculation

I want to calculate the implied volatility from the option data that I took from Bloomberg (call Option written on S&P500 index with the maturity of 19-Dec-2009 and strike of 1300), but volatility ...
1
vote
2answers
139 views

How market making in Index options is done?

I have been thinking about this one for last couple of days. With options on share we hedge on cash and the underlying equity as per Black-Scholes formulation. But I am confused on Index options. ...
1
vote
1answer
88 views

Black Scholes model: condition of payout function

Given: Consider a two-asset, continuous time model (B,S) where $$dB_t = B_t r dt, \quad dS_t = S_t ( \mu dt + \sigma dW_t)$$ Clearly, the martingale deflator is: $$Y_t = e^{(-r - ...
1
vote
3answers
328 views

Is this arbitrage?

Assume the stockprice as in the Black-Scholes model (Geometric Brownian Motion): $$S_t=S_0e^{(\mu-\sigma^2/2)\cdot t+\sigma W_t}$$ Wouldn't there be an immediate arbitrage opportunity, to just buy ...
1
vote
1answer
223 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 ...
1
vote
1answer
70 views

Is the Black-Scholes model price a bijection on the interval of static arbitrage free prices

Consider some stock with observed price $S$ and a call option on the stock with value $C$, time to maturity $T$ and strike $K$. Assume there is a constant, continuously compounded interest rate $r$. ...
1
vote
2answers
116 views

How can I make this portfolio self-financing?

$a_t S_t$ = number of shares ($S_t$ is stock price at $t$), $S_0 = 1$ $b_t \beta _t$ = saving account value , $d \beta_t = r \beta_t dt$, $r=$ interest rate So the value of the portfolio: $$V_t = ...
1
vote
1answer
68 views

Delta derivation from the expectation

I'm trying to understand the following transformation leading to Delta $\frac{dC}{dx} = e^{-r\tau} \mathbb{E}[ \frac{\partial}{\partial x}\text{max}(xY-K,0)] = e^{-r\tau} \mathbb{E}[Y ...
1
vote
1answer
69 views

What are the units of the variables appearing in a standard stochastic differential equation for a Wiener process?

The Black Scholes model assumes the following form for the Wiener process describing the evolution of the stock price S: $dS=\mu S dt + \sigma S dX$ Clearly $S$ ...
1
vote
2answers
328 views

Black-Scholes Equation - Riskless portfolio derivation

The following is a summary of the derivation of the Black-Scholes equation as given on wikipedia (http://en.wikipedia.org/wiki/Black-Scholes_equation#Derivation) - I have a question regarding the ...
1
vote
1answer
87 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 ...
1
vote
1answer
417 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 ...
1
vote
1answer
44 views

Connection between implied volatily and implied probability

I am reading some lecture notes about Black-Scholes (BS) option pricing. Since the BS-formula is not supported by observed data because of the dependence of the implied volatility on the strik and ...
1
vote
1answer
66 views

What is the distribution assumption of the black scholes model

As per wikipedia the Black Scholes assumption is: (...
1
vote
1answer
66 views

Why is the black-scholes model arbitrage free when σ>0?

I want to show that: if $σ$ is positive then there is no arbitrage in the model, even if $r > µ$. Whilst I have satisfied this for $ r > \mu$, I cannot see why the conditioning on $\sigma>0 $ ...
1
vote
1answer
60 views

Effect of massive volatility on BS formula

I am experimenting with very high volatility on the standard Black-Scholes formula. I set risk free to zero, time to expiry to 1, volatility to 1 (=100%), and underlying to 1. Then I simulate the ...
1
vote
1answer
523 views

Black Scholes formula with continuous dividend paying stock

I am reading the part of constructing B&S price for stock paying dividends. The simplest model used continuous yield dividend. But I can not see that rigorous in term of formulations. Firstly, ...
1
vote
2answers
180 views

Which risk free rate is assumed by market when pricing american options?

I'm just started with finance, so maybe my question is dumb or answered elsewhere. Please guide me to relevant materials. According to put-call parity more time to expiration means more difference ...
1
vote
2answers
241 views

Which interest rates to use for options pricing?

I am looking at the historical treasury interest rates and am uncertain which rates would be best to use for options pricing. Should I use 1 month, 6 month, 2 year? See: ...
1
vote
2answers
174 views

Bachelier model: number of stocks in replicating strategy

Given: Consider a two-asset, continuous time model (B,S) where \begin{equation} dB_t = B_t r dt, \quad dS_t = \mu dt + \sigma dW_t. \end{equation} The question is: Show that there exists a ...