# Questions tagged [black-scholes-merton]

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### Why a self financing portofolio equals to the value of a call option? [closed]

Why a self financing portofolio equals to the value of a call option? Actually, why we write $V(S,t) = a_tS_t+b_t\beta_t$? where $S_t$: stock price and $\beta_t$: bank account value , $V(S,t)$: value ...
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### Stability of Finite Difference method for Breeden-Litzenberger

I am trying to derive a risk-neutral density from European call option prices using a second order finite difference scheme. Let $C(K,T)$ be the price of a European call with strike $K$ and expiry $T$ ...
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### Black Scholes model without using Girsanov's theorem? It might happen?

We can calculate the stock price by the equation: $\frac{dS_t}{dt} = \mu dt + \sigma dB_t$,where $B_t$ is a Brownian motion. First i create a portfolio that consists of $\Phi$ units of stock share ...
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### Relationship between profit margins, historical volatility and implied volatility

In a scenario where no historic data exists in an option market, how would one come up with implied volatility for pricing of options, under the Black-Scholes-Merton model? My professor has ...
53 views

On March 2, a Treasury bill expiring on April 20 had a bid discount of 5.86, and an ask discount of 5.80. Calculate the best estimate of the risk-free rate to be used in valuing options with the Black ...
112 views

### Nonlinear Black-Scholes model Vs linear Black-Scholes

I am working on a project related to Nonlinear BS partial differential equation, with terms for transaction costs and/or discrete hedging. I have two questions: Is there any exact solution to the ...
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### Deriving implied volatility programmatically

I'm working on a project to calculate the value of options using Python. I'm using the Black-Scholes model, and I can get accurate results by plugging in a given ...
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### Alternative derivation of Black Scholes by Merton

I am currently reading the Theory of Rational Option Pricing (1973) by Robert Merton. In the paper, I encountered a section under the title "An Alternative Derivation of the Black- Scholes Model". I ...
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### In literature, is IV constantly adjusted during option delta hedging?

In a lot of literature, they like to compare the performance of buying an option, and then delta hedging either at that options implied volatility (IV) or the true future volatility. This is under ...
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### Option and probability of finishing in the money?

This seems to be another easy question but I am a bit confused. I know delta is a proxy for an option finishing ITM. Delta also happens to be N(d1) in the BSM pricing model. N(d1) usually is pretty ...
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### Modifying Basic Black Scholes Equation For Time Dependent Variables - Per Wilmott?

I am reading Wilmott's book and don't understand why he makes the following step to re-write the PDE. I get equation 8.4, that's just the typical PDE for a dividend yielding stock where r(t), D(t) ...
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### Risk-neutral pricing the “un”guaranteed benefits of an insurance policy

I'd love to know if the model of Black-Scholes-Merton could be used to anything that replicates the payoff of a call or option, for example: An insurance contract with participation ( meaning that ...
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### Value a structured note with Black-Scholes

Apologies in advance if this seems like a straight forward question but I'm really unsure how to go about it. Say I have the payoff for a structured note benchmarked against an index and I have a ...
I am reading a paper and get a problem here, the following terms are all from standard BS models. the paper says using the well known fact $$Se^{-q(T-t)}N^{'}(d1)=Ke^{-r(T-t)}N^{'}(d2)$$ here the ...