# Tag Info

11

The PCA analysis does not really tell you what the bonds do but it tells you how the rates move together. The variations of $n$ rates (i.e. 1 y, 2y, ...) are split up in (at first) abstract factors like $$\Delta R_i = \sum_{j=1}^n e_{i,j} f_j$$ where $\Delta R_i$ is the change in the rate $i$ and $f_j$ is factor $j$ and $e_{i,j}$ is the (factor loading=) ...

9

The majority of the movement in currencies is in the spot rates, rather than in the term structure. A 3-month rolling hedge would always be protecting against movements in the spot rates, no matter when they happen. Using your example, if the current EUR/USD rate is 1.3333, you might be able to get a 3-month forward at 1.3339. (Forgive me if I have the ...

5

Yes. Although sometimes people mean the Euro/Dollar currency pair which can cause confusion. Besides the daily mark-to-market, the counter-party risk is also removed through the clearing house for the futures. No. Eurodollar and FRA are not the same as swaps. A Eurodollar fixes an interest rate for a three month period in the future whereas a swap ...

4

Note that $\frac{F(0,s,T)}{F(0,t,T)} = \frac{T-t}{T-s}\frac{B(0,s)-B(0,T)}{B(0,t)-B(0,T)}$ and $\frac{F(s,s,T)}{F(s,t,T)} = \frac{T-t}{T-s}\frac{B(s,s)-B(s,T)}{B(s,t)-B(s,T)}$. Multiplying the numerator and denominator of the last expression with $B(0,s)$ and noting that $B(0,s)B(s,u)=B(0,u)$ (investing one Dollar for $s$ years and then for another $u-s$ ...

3

If you're asking what the FX Outright for 1M EUR/PLN is, given that table, then yes the answer is just outright = spot + fwd points, which is 3.4550 + 0.0079 = 3.4629 (you had the wrong column for your 1M value). Usually fwd points are quoted directly (i.e. not as an outright), using a divisor set by market convention. I expect EUR/PLN divisor to be 10,000, ...

3

for Japan, act/365 for the domestic market, and act/360 for the euroyen market. For swaps, fixed leg convention is 6m libor act/365, floating leg, if based on libor, is the 6m rate act/360, if tibor, then the 3m rate act/365.

3

The two are not equivalent, because of the cross-currency basis spread (CCBS), which became a risk factor in itself sice 2007, and does depend on term. This practically leeds to a difference in your constantly-assumed notionals (the notional is not constant anymore). What it happens is that you assume having a constant notional cross-currency swap that ...

3

it's easiest to see in terms of replication. The pay-off of a forward contract is $$S_T - K.$$ We can replicate this precisely and statically by buying one unit of stock, $S_0,$ and $Ke^{-rT}$ riskless bonds growing at rate $r.$ So its value today is $$S_0 - Ke^{-rT}.$$ This has zero value if and only if $K= S_0 e^{rT}.$ This value is then called ...

2

In my mind you are simply right: you arrive at $$f(t,S) = S(t) - K e^{-r(T-t)}.$$ Assume that $t=0$, so we are at the inception of the contract, then $$f(0,S) = S(0) - Ke^{-r T}.$$ If you choose $K = S(0) e^{r T}$ then the contract value at inception is zero. This simply means that the fair price for the forward is given by $K= S(0) e^{r T}$ which is ...

2

A very good and up-to-date question. Whether you use the LIBOR-rate or any other rate for discounting depends on what you decide to be the fundamental rates in the market. Before the crisis LIBOR-rates were mostly seen as the fundamental market rates (or the "risk-neutral" rates). After the crisis it turned out that these rates were not completely free of ...

2

The process must contain the spot price. The AnalyticEuropeanEngine will take care of calculating the forward price from the data you're passing in the process (in this case spot and risk-free-rate) and the maturity of the option. As implemented in QuantLib, though, The BlackProcess class assumes there's no dividend yield. If you want to model some kind of ...

2

The FRA A FRA is an agreement to exchange cash flows; the FRA in question is: Start 15/9/14 End 15/5/15 which is 242 days. USD Money Market quoting is Actual/360, so the accrual factor here is 242/360 = 0.6722. The FRA cashflows, therefore, are: on 15/9/14, Fix pays $\$1m * (0.6722 * 0.05) = \$33,611.11$, and Float pays $\$1m * (0.6722 * L)$, where L ... 2 Because the day count of your inquired date is 366 days: Hkd daycount is act/365 therefore 366/365 Usd daycount is act/360 therefore 366/360 $$\frac{7.7487}{7.7587} = \frac{1+r_2(\frac{366}{365})}{1+0.00965×\frac{366}{360}}$$ Solving for$r_2 = 0.8486. 2 You need to isolate the risk factors that impact your forward contract, which is your spot fx rate, and the two rates of each currency that underlies the forward contract. You therefore need to estimate the VaRs of each of those risk factors. You also need the correlations between the underlying risk factors. For example, a forward to buy USD in exchange ... 2 For the last question. We assume that \begin{align*} S_t = S_0 e^{(r-q-\frac{1}{2}\sigma^2)t + \sigma W_t}, \end{align*} whereW$is a standard Brownian motion,$r$is the interest rate,$q$is the dividend yield, and$\sigmais the volatility. Then, \begin{align*} X_{u+a}-X_a &= (r-q-\frac{1}{2}\sigma^2)a + \sigma(W_{u+a}-W_u)\\ &\sim ... 2 When you buy a forward you don't have to invest any money, so that's to your advantage in a world of positive interest rates. To charge you the same as the spot rate would be unfair, you would be "getting something for nothing", that is why the appropriate price for a forward is higher. It takes the interest rate into account, balancing things out. In ... 2 The forward priceF$for a forward contract, determined at the contract inception time today, is the price that the holder will pay at maturity$T$to buy the underlying equity. Then the payoff, at maturity$T, of the forward contract is given by \begin{align*} S_T-F. \end{align*} The present value of the contract is then \begin{align*} e^{-rT} ... 2 Strictly speaking, any risk-free interest rate can be composed into three components: The rate expectations component is the market's "true" expectation for future interest rate. A bond risk premium component: longer maturity bonds have higher duration risk than cash. Accordingly market participants will demand more compensation for taking on duration ... 1 The Heath-Jarrow-Morton representations of short interest rate models (such as Hull-White) will give you an expression for the evolution of the entire forward curve, but it doesn't make the problem any easier. The closed form ZC formulae you mention above are probably your best bet. 1 I will formalize my answer later. But one thing you will have to know is that the price of a forward contract will be a martingale under t forward measure, meaning the drift term is 0. This is not true under other measures. So the drift of the process depends on the measure you use to price the contract. 1 First, it's not true that a market sector is cheap whenever the forward curve lies above the par curve. In fact, whenever the yield curve is upward sloping, the forward curve will always lie above the par curve. Conversely, when the yield curve is downward sloping, forwards will always lie beneath the par curve. In the example you quoted, Ilmanen chose a day ... 1 Your discount factors are not inverted properly. Intuitively, df(0,T) should be a number between 0 and 1. For example, if r=0 then there is no discount so df = 1. If r > 0, then discount is going to be less than 1. Your formula for df will always be greater than 1. Check the formula given by the prof on the last slide titled "Term structure of ... 1 Always take care that you got the compounding frequency right. I recommend you take a deeper look at http://breakingdownfinance.com/finance-topics/derivative-valuation/forward-contract/ . You can download an excel file here and take a deeper look at the formula. You can also give in the compounding frequency as input. In case of doubt, or as a standard ... 1 First, it's not a 8% loan. The .08 interest on 1.6 is 5%. It appears that it is coming from theA (1) = 105$. 1 My 10 cents: Yes, the EUR is trading at a discount to USD. Think 100 - 2.8 = 97.2 for EUR, whereas 100 - 1.5 = 98.5 for USD so EUR is at a discount to USD. The calculation of premium and discount is in the forward pips. In your case it's spot - pips = forward 1.3195 - 0.0195 = 1.3000 So yes, the EUR cost in 6 months is$2500 / 1.3 = €1923.07 you agree ...

1

A good question... clearly you've read using 3 month forwards and see they are more liquid than other FX forward instruments. I guess that if there were only 3 month forward contracts in the market then by buying and selling the 3 months for different maturities, you could structure a set of 1 month forwards. so from today 21st Aug to hedge a short ...

1

Note NZD trade dates change at 7am Wellington which is 3pm Eastern at this time of year (not mid-day). Assuming your trade was on Friday after 3pm EDT then: - Trade Date would be Monday. - Value Date of Tomorrow would be Tuesday (a short dated forward) - Value Date of Spot would be Wednesday. You mention your value was Tuesday - I would therefore agree ...

1

I'm not expert on this field so may not able to answer your question precisely, but I can try the best to offer you some hints. According to the pure expectations hypothesis(PEH), forward rates provide unbiased predictions about future spot rates. Even if the PEH can be rejected, various scholars including Fama has provided evidence for the weaker form of ...

1

If I interpret your question below correctly: I don't understand why the cash flow for the EUR spot long position is being calculated the way it is. It makes no sense to me. Seeing as it is a spot rate why is it's cash flow not simply spot * 100 MM EUR notional ? You want to know why Jorion takes 100MM EUR * spot * 1/(1+eur_rate) instead of 100MM ...

1

Broadly, yes. An IMM dated swap is usually just a standard swap starting on an IMM date. However, there are a few closely related instruments which you could be asking about: IMM-anniversary swap - this not only starts on an IMM date, but also keeps to IMM dates for the roll schedule. It is a better match when hedging with IR futures, because an IMM-start ...

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