6 votes

Discounted price of an option

The process $Y_t:=(S_t-K)^+$ cannot be the price of a traded asset because of Jensen's inequality. Instead, it is the price of the option which is a martingale. In the Black-Scholes model, the ...
Daneel Olivaw's user avatar
4 votes
Accepted

Computing Derivative Security with Change of Numeraire

Hint: I think you need to use a tradable as numeraire. So the money market and the stock price are tradables. But $S_t^2$ is not a tradable. How to solve this: Notice that for $t\in[0,T]$ the claim $...
Frido's user avatar
  • 1,874
4 votes

How to find a risk-neutral measure for funds with management fee

Ja, good question. Bear with me for a moment: I used to price options on funds in the context of variable annuity pricing/hedging. Basically a VA is a fund (actually fund of funds) with a guarantee ...
Frido's user avatar
  • 1,874
4 votes
Accepted

Can the risk neutral pdf derived from Breeden-Litzenberger Method be used to calculate vega and theta?

No, vega cannot be derived in a model-free manner. The reason for this is because in contrast to delta and gamma, there are multiple definitions of vega, and an even deeper underlying reason may be ...
Frido's user avatar
  • 1,874
3 votes
Accepted

Is there a risk-neutral measure if there are two stocks with different drift terms?

Well there can definitely be a risk-neutral measure but only one of the processes is a tradable. For instance, consider the total return process of a stock $S_t$ $$ dS_t = \mu S_t dt + \sigma S_t dW_t ...
Frido's user avatar
  • 1,874
3 votes
Accepted

Verifying my understanding of replicating portfolio, hedging and option pricing

Under the risk-neutral measure, an European option is hedged with a replicating portfolio. The combined portfolio evolves at the riskless rate. For example, a short European call option with ...
KaiSqDist's user avatar
  • 785
2 votes

Why A Derivative With Intrinsic Arbitrage Cannot Be Valued & Hedged With Assets In Risk Neutral?

Valuing something to the writer vs valuing it to the buyer makes no difference. We just value the instrument. In this case the buyer surely would prevent the writer from collecting the fee, by ...
dm63's user avatar
  • 16.9k
2 votes
Accepted

Derivative pricing under $\mathbb{P}$

Assuming that $V(t)$ is the price process of some (perhaps implicitly) traded claim, it is correct. A typical interpretation would be the following: Given that the $T$-claim $\mathcal{X}$ is ...
Viktor Nilsson's user avatar
1 vote

Complete market without risk-neutral measure

Yes, you are right in that the second fundamental theorem of asset pricing needs the market to be arbitrage-free. Now, the model: This model is based on Nicolas Privault's Notes on Stochastic finance, ...
Confused Quant's user avatar
1 vote
Accepted

Forward Black Implied Volatility For Within Risk Neutral European Option Pricing

The 'model free forward implied volatility' is pretty useless for your purposes. First of all, it doesn't say anything about the price of future IVs, which you need, and worse it's pretty much ...
Frido's user avatar
  • 1,874
1 vote

Beta Weighting Deltas: What happens to the non-correlation part?

"At Beta=1 the underlying is expected to be as volatile as the index as well as move (more or less) together with the index." is not right. Beta has nothing to do with volatility, at-least ...
Arshdeep's user avatar
  • 1,905
1 vote

Martingale under risk neutral probability

You already have it. Risk neutral measure is one where tosses are still independent but each individual toss has probability of 0.5 up or down. Say you're at step n, with $S_{n}$ known. $E(S_{n+1}|F_{...
Arshdeep's user avatar
  • 1,905
1 vote

Floating Strike Geometric Averaged Asian Option Pricing

As Nick suggested, looking Espen G. Haug. The Complete Guide To Option Pricing Formulas. Mc- Graw Hill, 2007. P. Zhang. Exotic options, equation 4.105 shows a symmetric relation between a floating ...
nachofest's user avatar
1 vote

What is the risk neutral expectiation of an option price given a move in spot?

Your question is unclear / lacks relevant detail, but I suspect what you're really asking is what happens to the vol change when the spot change is given. Assume, as an example, the following dynamics:...
Frido's user avatar
  • 1,874
1 vote

Are all changes of measures for continuous diffusion processes given by the change of drift?

Although this is a quite old thread, but I actually had the same confusion as you pointed out in the question. I just found a relevant question that gives a reasonable explanation to the question: ...
Milk_Tutu's user avatar
1 vote
Accepted

Effect on variance of change of measure

(i) is true if measures are equivalent i.e. if $Pr(A)=0$ or $1$ in the first measure then it has to be the same in the other measure. Being equivalent is always true when you change measure through ...
Arshdeep's user avatar
  • 1,905

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