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2 votes
1 answer
74 views

Option implied risk neutral distribution vs BKM risk neutral moments

I am doing some research on the option implied risk neutral distribution and methods calculate it, and so far have come across two ways to do so. The first way is through the Breeden-Litzenberger ...
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  • 53
2 votes
1 answer
84 views

Show that the price of a LIBOR rate paid in advance is a linear combination of caplets

Let $L(t, T_1, T_2)$ be the forward LIBOR rate at time $t$ for the period $T_1$ to $T_2$. If a security pays some multiple of $L(T_1, T_1, T_2)$ at time $T_1$, how can we show that the price of this ...
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1 vote
0 answers
476 views

What is the risk neutral density and how is it estimated? [closed]

I don't understand the words "risk-neutral density". Please explain what it is, and how it can be estimated in practice. My guess would be that we have an underlying probability space $(\Omega, P)$. ...
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0 votes
1 answer
216 views

IVF and implied distribution of underlying in John Hull's book

There is a statement in John Hull's book Options, Futures and Other Derivatives 9th page 633 for the relation between ...
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  • 1,223
-2 votes
2 answers
411 views

Modeling stock performance in excel

I am trying to model the ending value of a stock after a certain number of years, I need it for a bigger project but I made this sample sheet to get help. This sheet is assuming that annual returns ...
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4 votes
0 answers
665 views

How to estimate option implied skewness and kurtosis in R

Suppose that i have data that for each day i have more than one option, either put or call. I.E. I have more than 20 put options and 20 call options for each specific day. What is the way to estimate ...
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0 votes
2 answers
3k views

What the implied distribution really is?

From volatility surfaces we have a implied distribution of $S_T$. This distribution is the real world distribution or this is a risk neutral distribution?
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  • 785
1 vote
0 answers
297 views

Pricing Exotic options

I am stuck at a assignment problem where I have to compute the price of an exotic option. I am given the values the prices of option $C(X;k) = E[max(0,X_T - k)]$ for different strike prices $k$ and ...
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7 votes
1 answer
11k views

Breeden-Litzenberger formula for risk-neutral densities

Based on this topic: How to derive the implied probability distribution from B-S volatilities? I am trying to implement the Breeden-Litzenberger formula to compute the market implied risk-neutral ...
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  • 431
9 votes
1 answer
2k views

Obtaining risk-neutral probability from option prices

Suppose I have the following data (for the current stock and option prices of the Bank of America) Strike Last IV Probability 4 8 5.43 0.5813566 0.0000000 7 11 2.45 0.2868052 ...
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  • 456
1 vote
1 answer
87 views

Is it possible to detect a belief that a security will peak and then decline by analyzing American options pricing?

Please forgive me if this is a dumb question. I know only the basics of options and their valuation, and this is a question I've wondered for some time without being able to find a satisfactory answer ...
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2 votes
1 answer
5k views

Implied state price density (Question 1 - derivation of the formula)

I came upon the term "implied state price density" in a couple of papers. As far as I understand the concept one basically tries to extract the "pricing density" from the market data. For the sake ...
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  • 3,337
1 vote
0 answers
245 views

Getting the actual distribution of a stock price at time T using implied volatility [duplicate]

Possible Duplicate: How to derive the implied probability distribution from B-S volatilities? Let's assume a stock price S, with volatility $\sigma$ constant, no dividend, and risk free interest ...
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5 votes
1 answer
311 views

Is it possible to estimate the correlation between an equity and its IV, purely from its IV skew?

If we know the options Implied Volatility (IV) skew for an equity, is it possible to calculate the probability of the equity moving, given a move in the IV? We can define IV skew as the difference ...
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