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3

I don't have much experience in the matter, but I've been doing some related literature research recently and I think these links can be helpful: A rather recent study from CME A (possible a bit biased) report by BlackRock A report by Lyxor (asset manager affialiated to Societe Generale)


2

You are correct that showing the self-financing condition for the BS-portfolio is not as straightforward as one may think: A portfolio $V_t(\alpha_t,\beta_t)$ (for stock $S_t$ and zerobond $B_t$) is self-financing iff: $$V_t=\alpha_tS_t+\beta_t B_t$$ It further implies $$dV_t=\alpha_tdS_t+\beta_tdB_t$$ To replicate a derivative $C(S_t,t)$ by a ...


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As always I recommend reading Rennie and Baxter for an introduction to option pricing that's not too technical and gives intuition about how it all works.


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I read the question as follows: You have one stock $S_0$ and after one period it either goes up to $S^+$ where the option takes the value $f^+$ or it goes down to $S^-$ where the option takes the value $f^-$. The bond grows from $B_0$ to $B_1 = B_0 \exp(r)$. Then you need to solve $$ a S^+ + b B_1 = f^+ \\ a S^- + b B_1 = f^- $$ for $a,b$ which are $2$ ...


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The current contract value is roughly 30k euros. The bidask spread is 1 tick, which equals 10 euros. Lets say you buy the contract and roll 3 times a year and then liquidate your position at expiry. You will hence pay 1 full bidask spread + 3 rolls, which if done via spreads with market orders, are equal to 1 tick each, hence you will pay 40 euros on bidasks ...


1

The concept of replication is indeed applied to IR products, after all they are also hedged in practice. However, in the equity world we start with the replicating portfolio and then arrive to the pricing formula. In contrast, for IR products we employ a convenient numeraire which helps us to arrive at the pricing formula directly (in a non-constructive and ...


1

For forward libor models, one can hedge interest rate options by using bonds. (Note that forward libor is a tradeable security under the forward measure). See http://www.columbia.edu/~mh2078/market_models.pdf For affine yield models (like Vasicek or CIR models) the inverse problem is the most useful. Given an interest rate process, I can compute a ...


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A unique state price vector does not have to exist for there to be no arbitrage. It sounds like the state price vector in question has infinitely many solutions. Try to reduce the price matrix to row echelon form and show that at least one state price vector exists.


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A variance swap can be replicated with vanilla European options. If you take derivative with respect to variance, you need to do the same thing on both sides. That is, you need also take derivative with respect to variance on those vanilla options. However, the resulting derivative is not the vega in the usual sense, which is the derivative with respect to ...


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I think I have figured this out. The key to the understanding is to think of the options' vegas as "key-strike vegas" compared to the var swap/replication portfolio's vega, which is analogous to "key rate durations of a bond portfolio" to the total effective duration of the portfolio.


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The variance swap's Vega that is equal to the variance notional refers to the realized variance. The Black-Scholes vega refers to the market implied volatility. Now if you want, you can estimate the realized variance at expiry from the volatility of the options (for instance taking the atm variance arbitrarily), and that's often what people do. But that's ...


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I think the title here is misleading. Let's go back to the BS world with $r=0$ to $a(S_t)=S_t \sigma.$ In that case, all you are saying is that you can replicate a call option by holding $N(d_1)$ units of stock at time $t.$ What does this have to do with the second equation? I am guessing that this is the price process of an asset of nothing option with ...


1

if you let the implied vol depend on K you get two terms the first is $N(d_2) $ but you get a correction term which is the slope times the vega $$ \frac{\partial C}{\partial \sigma} \frac{\partial \sigma}{\partial K}.$$ (see eg my book)



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