# Tag Info

22

Many of them are on my website at emanuelderman.com. Others I probably have anyway. Feel free to email me

8

I had read some of them; actually, it does not exist an on-line library that collected them (or, better, it existed here, but it seems the website does not work anymore). I reported here below some of them that you did not find: More Than You Ever Wanted To Know* About Volatility Swaps Model Risk The Volatility Smile And Its implied Tree Enhanced ...

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the problem is that the pay-off has discontinuous first derivative. Try a contract with pay-off that is twice differentiable and it will probably work. The problem is that all the value comes from the tiny number of paths within $\Delta S$ of the strike, and these paths have huge value. This is a well-known problem. As the bump size goes to zero, the ...

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As the manager of a mutual fund (not a hedge fund) you can only short treasury futures. So you take the one that is clostest in duration, look for an optimal hedge ratio and that's it. In my experience you have to leave liquidity risk open.

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The differential equation has a trend due to the interest rate. When you discount you take this trend away: $$\frac{d}{dt} (e^{-rt}Z_t) = -re^{-rt}Z_t + e^{-rt} \frac{d}{dt}Z_t = e^{-rt}\frac{1}{2}S_t^2\Gamma_t(\hat{\sigma}^2-\beta_t^2)$$ $Z$ doesn't appear on the rhs anymore and you can integrate e^{-rT}Z_T - e^{-r0}Z_0 = \int_0^T ... 2 Assuming zero interest, the put option has the price \begin{align*} KN(-d_2)-S_0N(-d_1), \end{align*} and delta -N(-d_1). When N(-d_1) units of stocks are shorted and invested in bonds, the total value in bonds is KN(-d_2), which is indeed greater than the option price. However, as you have shorted N(-d_1) units of stocks, your portfolio value is ... 2 Most index options are options on futures, so to delta hedge a single option position, you trade the corresponding future. For example, say you sell 10 delta 50 calls on the CME Emini S&P. To delta hedge them, you'd buy 5 CME Emini S&P Futures with the same expiry date as the options. As you say, you could hedge with the basket instead, but for ... 1 Instead of just considering a parallel shift of the whole volatility surface, you can decompose the surface into maturities/strikes domains, so called buckets and consider Vega buckets which are sensitivities wrt to bumps of each of these domains. The vol smile is often inter/extra-polated using a model calibrated to market prices, e.g. the SABR model or ... 1 we should first define some notation before discussing pricing. Let t_0 be initial time and  t_1, . . . , t_M be pre-specified exercise dates with t_0 < t_1 < · · · < t_M = T , the final maturity, and Δt = t_m−t_{m−1}. Without a loss of generality it is assumed exercise dates are equidistant. To price a Bermudan option, its value is split ... 1 I am not sure I fully understand your question. Options it just derivative contracts (wager) between two parties, there is no ‘real’ assets bought to support the +/- value change the option might have during its duration. When the exercise date is upon the option, and you are the winner, you are paid according to the WAMC of the index – e.g. 3.4% of your ... 1 This is a much simpler problem than stated, (assuming the correlation is positive). In 1 month you need to BUY 2mn of jet fuel. If Jet fuel prices go up, you lose money as it's more expensive. If jet fuel prices go down, you make money as it's cheaper. So to "hedge" your risk you will LONG the heating oil, as you are not in the business of speculating on ... 1 It's a combination of too few sample paths and/or too small an increment. Your estimation error on the price is magnified by the dS^2. Try using a larger sample or a larger increment. Alternatively, you can use a multiplier instead of a fixed increment; in my experience, it usually yields better results. 1 You have already agreed to pay QK EUR at T to receive Q units of A. If you sell Q lots of F^A(t,T) then you will receive Q F^A(t,T) EUR and deliver Q units of A. The combined flow is now just in EUR: at T you receive a net of Q(F^A(t,T)-K) EUR. You can hedge that by selling Q(F^A(t,T)-K) of F^{FX}(t,T). Then with both hedges, the net ... 1 That seems to be a nice paper but I haven't worked through it completely yet. As I understand it, the goal is to replicate the holding (by an investor) of an European option using an American option, stock and bonds in a self-financing manner. As the value of the underlying changes this requires rebalancing of the option and the bond, i.e. hedging. Since ... 1 This sounds like quadratic hedging. If you have the return of the assets r_X and r_Y with negative correlation \rho between the two (we could think of bonds and stocks) and more variance in one of them then the problem of weighting the two by w is (assume zero expected returns for ease of presentation) \text{risk} = E[(w r_X + (1-w) r_Y)^2] ...

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