18

The trick here is that you're not asking about $\mathrm{Var}\left(\frac1X\right)$. Imagine one currency is a stock $S$ and the other a stock $Q$. Then the volatility of the exchange is the square root of: $$\mathrm{Var}\left( \ln\left(\frac SQ\right) \right) = \mathrm{Var}\left( -\ln\left(\frac QS\right) \right) = \mathrm{Var}\left( \ln\left(\frac QS\right) \...


8

OpenGamma has a good resource for market conventions.


8

Within the fixed income space, there's a lot of literature on PCA trading. The first 2-3 principal component factors (PCs) can typically explain 90-99% of the total variances in yield curve movement. It's also nice, because the first PC looks like a change in the overall level of the yield curve, the second PC looks like a slope change, while the third ...


6

Today (1 day after the fact) the following headline appeared in the Financial Times: "September Fed rate lift-off put in doubt, Fallout from China’s currency move turns market mood". If true, this would certainly explain why the USD declined (i.e. the interest rate rise that everyone expected has been postponed). However, in my experience it is very hard to ...


5

Certain regulations in a country might inhibit the values of a unit of currency from being the same within the borders of the country and outside. There might be foreign exchange or banking regulations. For example, the eurodollar rate is different from the dollar inside the US, since there are reserve requirements dictated by the Fed. Basically, same ...


5

The most universal name that any "currency (pair)", "equities" or "futures" falls under is either a product or an instrument. In some ways I prefer product because you can have 2 exchanges allowing you to trade BTC-USD or AAPL, these are fundamentally the same fungible instrument, but these are 2 different products because they have different trading fees. ...


5

The ATM is an outright position (long 50 delta put and 50 delta call) so the main exposure is vega. It is the riskiest of the three, and demands a higher bid-offer spread from market makers to compensate them for the additional risk. The RR is a spread position (long 25 delta call, short 25 delta put) with zero vega, the main exposure is skew. Because the ...


5

A reference entity (the debtor that might have a credit event) does not have any currency denomination. A reference entity might have many outstanding debt instruments. Each instrument is denominated in some currency. You need to choose one debt instrument as the reference obligation for the CDS contract. You choose the currency in which the CDS contract ...


5

Simply put, Russian banks (and other institutions) had local assets and hard-currency liabilities. Local assets lost value not only because they were denominated in a currency that unexpectedly depreciated by a lot, but also the equities market crashed, and a lot of the corporate debt defaulted following the government default (local-currency debt). Hard-...


4

It's because of onshore capital controls; units of currency cannot freely enter and leave the country and so currency held onshore (within the domain of the capital controls) is not fungible with currency held elsewhere. Hence, due to the limitations of arbitrage, those two currencies are not tightly coupled. They are related, since actual physical onshore ...


4

Position here is the residual amount of one or other currency at the end: You gave us: Time | Amount | Rate | t1 100 1.2636 t2 -1000 1.2599 t3 200 1.1612 Assuming the Amount is amount paid in USD, and the rate is EUR/USD: Time | Amount | Rate | EUR balance | USD balance t0 0 0 t1 ...


4

To answer this question, lets dive into some of the factors that generally determine foreign exchange rates. I've outlined the two of the most widely discussed factors below. Current account balance An economy's current account is a component of an economy's balance of payments and is a measure of the economy's financial transactions with the rest of the ...


4

You have forgotten the combinatorial factors for binomial probabilities on your terms. You need $$ {n\choose k} p^n(1-p)^{n-k},$$ not just $$ p^n(1-p)^{n-k}.$$ The second term should have a factor of $6$ and the third should have a factor of $15,$ etc.


4

I think you have the answer in the comment you made. I will again explain with the inverse exchange rate S, and let me represent the forward price of this exchange by f. And let me represent the first time by 0 and the second by t, no more multi-period as in the previous answer! Now the unhedged asset value at next step will be: $P_t S_t$ We want exposure ...


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

Yes, you can use e.g. the ECB daily official foreign exchange rate data as a reliable and consistent daily timeseries. ECB does a fixing at 14:15 CET, by some methodology they call a "daily concertation procedure". I don't easily find a description of the details (are they considering only traded prices, or bids and offers? How long of a time window ...


3

Perhaps this paper by Hyun Woo Byun and coauthors is what you're looking for: Using a Principal Component Analysis to develop Multi-Currency Trading algorithms in the FX market They apply principal component analysis to a currency basket of 9 pairs with a 2 month rolling window. In a second step, various techniques (logistic regression, decision trees, ...


3

Compounding the monthly excess returns won't provide the annual excess return. You need to compute the difference between the annual return of the portfolio and the annual return of the benchmark. To illustrate this let's look at an example. Consider the following two situations: The benchmark performs well with a $2\%$ return each month; The benchmark ...


3

It costs 0.03 dollars for the option to (sell 1 pound/buy 1.5 dollars. Now divide everything by 1.5: It costs 0.02 dollars for the option to (sell 2/3 pound / buy 1 dollar). Now convert to pounds at spot rate: It costs 0.0133 pounds for the option to (sell 2/3 pound / buy 1 dollar). Done


3

Since I'm not a FX guru I need to prove the comment of @alex c A USDJPY 100 call on one dollar has payoff: max(0, FX-100) Yen where FX=USDJPY at maturity. A JPYUSD 0.01 call on one Yen has payoff max(0, 1/FX - 0.01) Dollars = 0.01/FX * max(0,100 - FX) Dollars = 0.01 * max(0,100 - FX) Yen which is the same as a USDJPY 100 put on 0.01 dollars, as ...


3

There is no contradiction and basically no ambiguity. Furthermore, the kind of product (linear or non-linear) has no bearing on the question. It is really only a question of basic calculus. Let us call the three FX rates $x, y, z$ which satisfy the relation (or constraint) $z=xy$ and your product $P$, which is a function of $z$ only. You can interpret $P$ ...


3

$S(t)$ is the stock nominal price. Nothing precludes you from modeling a stochastic differential equation for the stock real price, but that would not be practical for pricing derivatives, as options fixed strike prices would have to be divided by the CPI to be converted to real prices, thus requiring joint modeling of the stock real price and the CPI. ...


3

Usually you think of it as a non-arbitrage relation. The usual formula that should hold in equilibrium (in absence frictions) is the covered interest rate parity. However, for ease of intuition let's start with the uncovered interest rate parity: $(1+i_{domestic}) = \frac{E_t(S_{t+k})}{S_t} (1+i_{foreign})$ This formula basically says that two investment ...


3

When in doubt, write down a diagram like this: AUDUSD: price of an AUD measured in USD = 0.68 Exchange Exchange Country Today Interest Rate in Future ---------- ----- ------------- --------- USA: 0.68 r_usd -----> 0.68*exp(r_usd*T) ...


3

The way central banks do this is to calculate the Effective Exchange Rate for the country in question. Basically this is a weighted average of the other currencies, with the weights chosen to represent the importance of each foreign country in the international trade of the domestic country. For example for the United States, the Fed has defined the Broad ...


3

Try the BIS Triennial FX Survey, latest was last year. https://www.bis.org/statistics/rpfx19.htm E.g. https://stats.bis.org/statx/srs/table/d11.4?o=8:TO1,9:TO1 (table showing "OTC foreign exchange turnover by instrument, counterparty and maturity in April 2019, "net-net" basis") EDIT: you could also try https://www.bankofengland.co.uk/...


3

So, a future is basically like a forward. $F_0(T) = S_0e^{T(r_{f,T}-r_{d,T}+x_T)}$ The longer dated you go, the more you have exposure to the stuff in the exponential (rates in the two currencies, and the xccy basis $x_T$). That's a trading choice: do you want to trade pure spot FX (or close to it), or the forward (for which maturity?) The answer of ...


3

It's a unit of account (for the IMF and other international bodies') purposes. As well as just a basket of the most liquid and transferable currencies that reserve managers will all hold anyway in their normal course of business. It doesn't "move" FX markets. The measures as I understand them are: = basic liquidity and transferability (which is why ...


3

Some additional comments to @Jeremy909. That "problem" is one reason why logs are so useful. See Reason 2: The log difference is independent of the direction of change. However, I think it is not clear from your question if you think about volatility of the price series itself or volatility of returns. There are a bunch of ways historical ...


3

According to the finance data disclaimer (https://help.yahoo.com/kb/exchanges-data-providers-yahoo-finance-sln2310.html) the source for fx rates is the ICE data service.


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