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4

To continue from uness' answer (edit: just seen the OP was very old, but will leave here anyway!) . The greeks will be every element of market risk to which the the CVA is sensitive. Writing in words for celerity: A CVA is a credit linked option on the underlying instrument. You are sensitive to the credit default- (specifically the swap obligation payment ...


4

CVA is a price. Just like any price, you compute its sensitivities (greeks) and then use financial products to bring them as close to zero as possible. It's not possible to derive a hedging strategy just by looking at the CVA figure, it's like asking what the hedging strategy of a product is if its price is USD 1M... You need the CVA greeks. The ...


4

An Investment Bank earns a profit by selling you an option at a slightly higher price than the theoretical price, or buying it back from you at a slightly lower price. They call this "earning a spread". Then they hedge the option, so as not to make any [further] gains or losses on it (other than the risk free rate). Another way they could earn a profit is ...


4

I'm no special expert on options and their Greeks. However, I have had a decade plus experience of almost-daily discussions with a bank derivatives desk, on pin risk and the behaviour of autocallable, cliquet etc. structures. You are correct that a gamma hedge would require an options as opposed to underlying hedge. However, the traders' obsession with gamma ...


4

Step 1: Know your distribution Since $\int_0^t W_s\mathrm{d}s\sim N\left(0,\frac{1}{3}t^3\right)$, we have \begin{align*} S_t &= S_0 \exp\left( rt-\frac{1}{6}\sigma^2 t^3 + \sigma \int_0^t W_s\mathrm{d}s \right) \\ &\overset{d}{=} S_0 \exp\left( rt-\frac{1}{6}\sigma^2 t^3 + \sigma \sqrt{\frac{1}{3}t^3} Z \right) \\ &\overset{d}{=} S_0 \exp\left( ...


3

Short answer: Do not use BS for AC Long answer: There are plenty of question here about this already. Typically it is priced via Monte Carlo but that is not a model, just an implementation of some model (LV, SV, SLV). Standard would be to use SLV but even there are issues with decorrelation and bilocality if you look at basket AC (which are very common). ...


3

I will work through a detailed example. I hope it helps. Suppose for simplicity that you are trying to hedge the interest rate risk of one simplistic debt instrument. Suppose that the obligor owes you USD 10 million and promises to pay fixed 10% annual coupon, and to repay the principal in equal installments in years 4 through 7. So the cash flows look like ...


3

Let's use the following returns matrix, X 2Y 5Y 10Y -------------------------- 0.0143 0.0910 0.1451 0.1791 0.3505 0.4588 0.0572 0.1358 0.0120 0.0357 0.1809 0.2884 -0.0571 -0.1096 -0.0719 0.0286 0.0710 0.1319 0.0429 0.1806 0.2754 -0.0357 -0.0579 -0.1075 0.0714 0.2513 0.4304 -0.0214 -0....


3

This is just like any other option. For example, if you are trading an IBM option, you hedge with IBM stock, which doesn't expire at all, (obviously). You then sell your hedge in the gamma-storm that enuses at expiry. For longer term options where you have an expiry that goes way past the futures you have two choices: Trade the rolls periodically and/or ...


2

This is a resource you may want to look at. https://personal.vanguard.com/pdf/ISGHC.pdf Additionally, this books seems good for this particular topic: Risk Without Reward: The Case for Strategic FX Hedging. Also, take a look at Advanced Bond Portfolio Management: Best Practices in Modeling and Strategies edited by Frank J. Fabozzi, Lionel Martellini, ...


2

I would put the answer a bit differently: In the end you care about the price, don't you? If you sell the bond then it is bad if you can sell it for less. No matter what the yield is. E.g. if you have assets in a mutual fund then investors enter and leave the fund and you probably have to sell and buy assets (and there are more clever ways of cash ...


2

If the aim of the hedge is to make the portfolio insensitive (as much as possible) to small movements in the yield, then the question that needs answering is the following: If the yield of the hedge moves by $x$, by how much did the yield of the bond move? The answer is given by the correlation between yield movements between bond and hedging instrument, ...


2

The concept of covered interest rate parity (CIP) dictates that the forward price should equal the spot price multiplied by the ratio between domestic and foreign interest rates: $\ F = S*(1+i_d)/(1+i_f) \\$ In practice CIP means that the outcome of buying an FX forward should be equal to borrowing money in domestic currency (at the domestic interest rate),...


2

I'll try to give some views on this, I hope it helps bringing some closure to your question. You seem to relate consensus to "theoretical prices". I think this is a bit misleading. I view consensus as nothing more than the average view across the street for market factors, e.g. the correlation between the Korean KOSPI and the Spanish IBEX, the ...


2

Achieving gamma neutrality refers to your whole portfolio situation. If you have a portfolio $P$ made up of $n_S$ shares of stock $S$, and of $n_1$, $n_2$ option calls $C_1$, $C_2$ on $S$ (options 1 and 2 differ in strike price or expiration), pursuing a gamma hedging strategy would imply to achieve neutrality on the Delta $\Delta_P$ and Gamma $\Gamma_P$ ...


2

re 1 and 2: You might want to Google something like 'volatility decay' or 'volatility drag' for leveraged ETFs. re 3: a quick look at http://pages.stern.nyu.edu/~adamodar/New_Home_Page/datafile/histretSP.html suggests the long-term average return for US stocks is ~11.6% pa. You're proposing giving up ~5% pa to hedge. Not clear that's a good idea. also re 3: ...


2

\begin{align} d \left(e^{-rt} \left(V^i - V^a \right)\right) &= \left(d e^{-rt} \right) \left(V^i-V^a \right) + e^{-rt} d(V^i - V^a)\\ &= (-e^{-rt} r dt) (V^i - V^a) + e^{-rt} (dV^i - dV^a) \\ &= e^{-rt} [ -r (V^i - V^a)dt + (dV^i - dV^a) ] \end{align} So multiplying everything by $e^{rt}$ gives the result.


1

St. Louis Fed Financial Stress Index - https://fred.stlouisfed.org/series/STLFSI2 There are others (e.g. from the sellside) but this is publicly available. EDIT: looks like some of the sellside indicators are published on Bloomberg (no permissioning required), e.g. GFSI Index from BAML.


1

If we work through this practically, a hypothetical derivative under IFRS9 cash flow hedge should be representative of the underlying, henceforth the MTM CCS must be mark to market on the currency side opposite to that of the hedged instrument. For example, a EUR corporate might issue a yankee bond in 100mm USD and cross currency swap it back to EUR under a ...


1

Without a risk free investment, the efficient frontier is described by a hyperbola, as you have already suggested. Efficient Frontier: Tour de force Given asset covariance matrix $\Sigma$ and the full-investment condition $w_1+\ldots w_N=1$, it can be traced out by optimising $$ \min_w w^T\Sigma w \quad s.t. \quad w^T\mathbf{1}=1 \quad \mathrm{and} \quad ...


1

Note that \begin{align*} Call_{\rm BTC}=\frac{1}{S}Call_{\rm USD}. \end{align*} The premium adjusted delta $Delta_{PA}$ is defined as the change of $Call_{\rm BTC}$ with respect to the change of the spot in BTC, that is, \begin{align*} Delta_{PA} &= \lim_{\Delta S\rightarrow 0}\frac{\Delta Call_{\rm BTC}}{\frac{\Delta S}{S}}\\ &=\lim_{\Delta S\...


1

So, basically, the answer is no. For capital requirements Basel has three categories: a) Counterparty Credit Risk b) Market Risk c) Operation Risk All RWA calculations are additive. If your hedge is with the same counterparty then it likely offsets a) and b) and possibly c). If your hedge is only a market hedge then it will only offset b) and possibly ...


1

Most of the literature in Finance assumes continuous hedging which is just practically impossible. Minimum variance hedge ratio assumes the same. Unless you’re a bank or HF that can cost effectively re-hedge portfolios regularly, you’ll never get anything near a perfect hedge. For a retail investor I would say to avoid time evolving betas like with Kalman ...


1

If you purchase a Stock today in USD you will model that it has some value in USD in the future, $$ S_{t, usd} = S_{0, usd} + W_{t, usd} $$ where $W_{t, usd}$ is some random motion, possibly with drift, such that $E[W_{t, usd}] = \mu$. Ideally you would exchange $S_{t, usd}$ at maturity, so this is the amount of notional that should be translated to ...


1

The two formulations seem to be exactly the same. If I take the equations from the first method: $w_{D1}*\Delta_{D1} + w_{D2}*\Delta_{D2} = -2$ $w_{D1}*\Gamma_{D1} + w_{D2}*\Gamma_{D2} = -3$ And substitute for delta and gamma of the two options: $-w_{D1}+ 5 w_{D2}= -2$ $2w_{D1} -2w_{D2} = -3$ which after shifting the constants to the left becomes ...


1

Intuitively, this is the "coupon effect" at work – when the yield curve is upward sloping, lower coupon bonds have higher yield and their yields move up more when the overall curve shifts up (all else equal). The opposite is true when the yield curve is downward sloping. We'll focus on when the curve is upward sloping below. I think it's probably best to ...


1

1) You didn't specify whether you're interested in ex post or ex ante risk analysis. But in either case, beta / correlation to the relevant stock market index is really important for long/short equity funds. They could be just leveraged beta plays and providing no alpha, or they could be market neutral and providing only alpha. Looking at exposure or ...


1

So after much calculations, this is the approach: In 1 year you need €1,000,000, how much do you need currently ($x$)? If the euro interest rate is at 6%, $$ x\ \times\ (1+6\%) = x(1.06) = €\ 1,000,000$$ $$ \begin{align}x\ = \frac{€\ 1,000,000}{1.06} \newline \therefore\ x\ = €\ 943,396.22\end{align}$$ With the current spot rate, we can convert € 943,...


1

Ito's lemma gives $$dF = \left(\frac{\partial F}{\partial t}+\frac{1}{2}\frac{\partial^2F}{\partial S^2}\sigma^2 S^2\right)dt + \frac{\partial F}{\partial S}dS = adt + bdS $$ Using the usual rules, e.g. $dz^2 = dt$, we get $$ dS^2 = \sigma^2S^2dt,$$ $$dF^2 = b^2dS^2 = b^2\sigma^2S^2dt,$$ and $$dSdF = bdS^2 = b \sigma^2S^2dt,$$ so this gives $$dP^2 = dS^2 +...


1

What you call additional basis risk is unpredictable. It may win or lose in rolling strategy against buying 1 year futures once. But what is measurable is bid/offer spread. In 1 y contract it might be significantly wider that in quarter futures, even considering that you sell 4 times and buy 3 (lose 7 half spreads).


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