# Questions tagged [black-scholes-merton]

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### Black Sholes Options Pricing Clarification Questions [closed]

I am interested in pricing American Call and Put Options using BSM and I am new to exploring options prcing. I have some questions here that would really remove the confusion I have on how to more ...
67 views

### Black Scholes informal derivation - question about a term in the equation [closed]

I am wondering what the term S means in the equation I have circled? I am not sure how to interpret it.
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### Hull's book - Futures option's rho

In Hull's book (9th edition), on page 420, in table 19.6, it says rho of a European call on an asset with yield $q$ is $$KTe^{-rT}N(d_2)$$ Below it says we can compute greeks of European options on ...
256 views

### Boundary conditions Heston's stochastic volatility model

I'm trying to derive the following boundary conditions for heston's stochastic volatility model. This is p. 289 of Shreve's Stochastic calculus for finance \begin{align} c(T, s, v) &=(s-K)^{+} \...
92 views

### 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 $T$ ...
164 views

### 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 ...
70 views

### 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 ...
193 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 ...
140 views

816 views

### 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 ...
124 views

### 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 ...
131 views

### 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 ...
2k views

### 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 ...
254 views

### 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) ...
48 views

### 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 ...
92 views

171 views

### 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 ...