# Tagged Questions

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

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### How to price this option using the Black Scholes model?

I have a question regarding regular option pricing. In the standard Black-Scholes model, with interest r and volatility $\sigma$, I have to eetermine the arbitrage free price at time $t$ of an ...
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### Formula behind pandas.Options() implied volatility

I noted that implied volatility (IV field) from pandas.Options class is very different (especially, for out of money options) than what I compute with Black-Scholes model. (risk free rate is pulled ...
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### Kurtosis in asset logarithmic returns

Assets such as stocks usually display kurtosis in their logarithmic returns. However, their logarithmic returns in a time interval $n$ are the sum of smaller logarithmic returns in $1/n$ time ...
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### How to compute the volatility for the Merton's Model for Private firm?

After one day of research i did not figured how to compute the input volatility for PRIVATE COMPANY in order to calculate the PD. My goal is to compute the PD of each of my company in my portfolio, ...
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### is there an analytical proof that vega-neutral also provides (gamma & theta) neutral?

I've read an answer here that say if your security has vega, then it has gamma and theta. is there an analytical proof that vega-neutral also provides (gamma & theta) neutral?
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### Can American options with no dividends and zero risk-free rate be treated as European?

Let's say you've got American options on a future of a stock index. There are no dividends, and no risk-free rate either (assume $r=0$). Can these options then be treated as European from the ...
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### Why t (time) in Black Scholes & Binomial defined as year?

What's the logical/scientific explanation for Black Scholes & Binomial using year rather than second (SI standard for time) ?
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### 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 ...
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When valuing a vanilla option on an index (eg FTSE 100), should we take index dividend yield into account? $$c=Se^{-q\tau}N\left(d_1\right)-Ke^{-r\tau}N\left(d_2\right)$$ $$d_1=\frac{\ln\left(\... 1answer 407 views ### Analytical solution for a modified Black-Scholes equation Recently, a modified Black-Scholes equation was proposed (Zheng), namely Please consider the case when$$\sigma \left( S,t \right) =\sigma\,{S}^{k/2}$$and with the European put option Using ... 1answer 103 views ### Option writing optimal sell time When selling options, e.g. a straddle I read often the optimal time for selling options is 30-40 days until expiration. For me intuitively the optimal time would be around one week until expiration ... 1answer 124 views ### Gamma derivation from the expectation I am trying to derive Gamma from the expectation principle (differentiating under expectation sign). I understand these steps \frac{d^2 C}{d x^2} = e^{-r\tau} \mathbb{E} [ \frac{\partial}{\partial x}... 2answers 257 views ### Why N(d_1) and N(d_2) are different in Black & Scholes I'm struggling to understand the meaning of d_1 and d_2 in Black & Scholes formula and why they're different from each other. As per the formula,$$C = SN(d_1) - e^{-rT}XN(d_2)$$which ... 1answer 73 views ### Connection between implied volatily and implied probability I am reading some lecture notes about Black-Scholes (BS) option pricing. Since the BS-formula is not supported by observed data because of the dependence of the implied volatility on the strik and ... 2answers 309 views ### Implied Volatility Calculation I want to calculate the implied volatility from the option data that I took from Bloomberg (call Option written on S&P500 index with the maturity of 19-Dec-2009 and strike of 1300), but volatility ... 1answer 92 views ### Is the Black-Scholes model price a bijection on the interval of static arbitrage free prices Consider some stock with observed price S and a call option on the stock with value C, time to maturity T and strike K. Assume there is a constant, continuously compounded interest rate r. ... 0answers 121 views ### Black-Scholes formula with deterministic interest rate and dividend yield Does any one have the Black-Scholes formula for a European call with time-dependent but deterministic interest rate and dividend yield ? 4answers 306 views ### Why is C(t,S_t)/B_t a martingale? In the derivation of the Black-Scholes formula given by Joshi (extract below), he says C(t,S_t)/B_t is a martingale. Why? I understand this can be deduced from the Black-Scholes PDE since the drift ... 1answer 155 views ### Beta between stock and option In Black Scholes model I would like to compute$$ \beta_K = \frac{\mathrm{cov}(C_{K,T},S_T)}{\mathrm{cov}(S_T,S_T)} = \frac{\mathrm{cov}((S_T - K)^+,S_T)}{\mathrm{cov}(S_T,S_T)} $$with respect to say ... 2answers 651 views ### The greeks: where do they come from? I’m studying the BSM model and having a look at the greeks. I was reading Derivatives, by Paul Wilmott, and he gives the closed form solutions without making the reader see where these solutions come ... 2answers 665 views ### good R package for vectorized option pricing I am using for now the package fOptions but it doesn't allow for vectorized computation of black76 prices and delta. Which package can be used to do that? As noted ... 3answers 190 views ### Arbitrage bounds for Black-Scholes In some implied volatility code I came across, there is a check to ensure there is no violation of the arbitrage bounds based on the inputs to the method. For the call option, if$$P < 0.99 * (S-...
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 ...