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17

Here is a short list (to be edited and improved - community wiki) : Standard brownian motion (also called Wiener process) for which: $d\, W_t \sim \mathcal N(0, \sqrt{d t})$ Geometric brownian motion, used in the Black-Scholes model (1973): $d\,X_t = \mu X_t\,dt + \sigma X_t\,dW_t$ Constant elasticity of variance ("CEV") model (1975): $d\,X_t=\mu X_t dt + \...


12

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 ...


11

You kind of answered the question yourself. Precisely because different market participants use different inputs to their pricing models, it is much easier to quote one single input (implied vols) than the output of 5 different inputs (BS option price). What is important is that you clearly differentiate between quoting and agreeing on the trade vs. the ...


9

Assume you have an USD-EUR Cross Currency Swap (3M-FloatUSD+SpreadUSD vs 3M-FloatEUR+SpreadEUR) (spread on USD side is usually zero), collateralized by USD-OIS (Fed Fund) I assume you know the USD-OIS discount curve, then you know the discount curve for USD cash flows. I further assume that you know the USD-3M forwards collateralized w.r.t. USD-OIS (from ...


9

The fx market, contrary to most other asset classes is an almost entirely fragmented over-the-counter market, aside the very small number of fx futures that are trading at dismal liquidity levels. Therefore, you will not encounter a single serious liquidity provider that will take a stab at estimating total traded volume in any of the currency pairs. Having ...


8

The formula $F^X(t,T) = E_t^d\left(X_T \right)$, under the domestic risk-neutral measure, is problematic. Note that, at time $t$, the forward exchange rate $F^X(t,T)$, for maturity $T$, is the exchange rate such that the payoff $X_T-F^X(t,T)$ has a zero value at $t$. That is, \begin{align*} B_t^d E_d\left(\frac{X_T-F^X(t,T)}{B_T^d} \mid \mathcal{F}_t\right)=...


7

I work extensively with currency models and have to admit there is not much in the public domain regarding recent published research that may satisfy your needs. Some of the below mentioned models incorporate stochastic components but please keep in mind that most research on currencies focuses on fundamentals (such as balance of payments) and depending on ...


7

Ask minus bid has nothing to do with the mid price - it is the spread. Generally you see a collection of bid/offer orders resting on different price levels. In the simplest case, you just see one bid at price $p_b$ and one offer at price $p_a$. In this case the mid price is $$ p_m = \frac{p_a + p_b}{2} $$ That's all there is to it - you don't need to "...


7

An FX Swap can be described as "borrowing in one currency and lending in another". When put this way it is clear that it has something to do with interest rates in the two currencies. You will be very happy if the i.r. in the currency borrowed rises and the i.r. in the currency lent falls the day after you do the deal, because you will have locked in more ...


7

The top chart is called a 'candle stick chart' or 'OHLC candlestick' or 'OHLC bar chart' http://multicharts.com/trading-charts When the price goes down during a time interval (from O to C) the box is filled in orange, when the price goes up it is green bordered with black inside. The exact colors are a matter of taste, as long as they are clearly different ...


7

Be careful of your rate conventions! The issue here is that all your rates are expected to be in units of domestic vs 1 unit of foreign. So for example USDCAD is 1.3347, you really need to be using 1/1.3347 = 0.749 USD per 1 CAD. So, your inputs need to be $$ \begin{align} S &= 1 / 1.3347 \\ X &= 1 / 1.3338 \\ R_d &= 0.75\% \\ R_f &= 0.50\% ...


6

Most common practise is to linearly interpolate. Log-linear would be wrong; forward points are commonly negative, and are merely a delta on the Spot. Closer would be log-linear on the outrights (Spot plus forward points), but even that is not worth bothering with. If you have some idea of the shapes of the underlying yield curves, you can work out which are ...


6

I have a little more informations, so let me share it with you. Even though I think that the frameworks I presented in my question are both corrects (i.e. aribtrage free), it happens to be the case that the market seems to have more "structure". Here is a methodology that allows to retreive market quotes and which is the same as BBG (which is the best ...


6

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 $r_2 = 0.8486$.


6

The time to expiry is required, but it's included in the inputs: the two discounts $e^{-rT}$ and $e^{-qT}$ and the standard deviation $\sigma\sqrt{T}$. You might argue it could be documented more clearly, and I might agree with you.


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 ...


6

What happened was totally unexpected end of peg against the euro @ 1.2CHF regime that Swiss central bank aborted. See some articles about it. As far as I know nobody in the markets knew, there was no indication whatsoever.. In terms of management, I'm afraid lots of people got heavy losses, particularly banks (Austria, Poland, Hungary) - lots of Swiss loans ...


6

Yahoo has changed their site structure. The new download URLs look like this: https://query1.finance.yahoo.com/v7/finance/download/MSFT?period1=1463461200&period2=1494910800&interval=1d&events=history&crumb=lHxk.yfuuzZ These links originate from pages like this: https://finance.yahoo.com/quote/MSFT/history?period1=1463461200&period2=...


6

Dukascopy offers historical tick data. Through their historical data website you can download what you want, but registration is required, and lots of manual clicking. However if you are comfortable with scripting, you can directly download the tick data yourself. The URL pattern is http://www.dukascopy.com/datafeed/{currency}/{year}/{month}/{day}/{hour}...


6

$$F = Spot \times e^{(\text{local interest rate} - \text{foreign interest rate}) \times T}$$ where $Spot$ = AUD per dollars. $T$ is the time to maturity of the contract (in years). So for example if the contract expires in 1 year and a half, $T = 18/12 = 1.5$.


6

Let $P^d$ and $P^f$ denote the respective USD and EUR risk-neutral measures. We assume that, under the USD risk-neutral measure, \begin{align*} dS_t = S_t \Big(\big(r^d-r^f \big)dt +\sigma dW_t \Big), \end{align*} where $r^d$ and $r^f$ denote respectively the USD and EUR interest rates, $\sigma$ is the constant volatility, and $W_t$ is a standard Brownian ...


5

Fatih Yilmaz, formerly of Bank of America (currently BlueGold), has a piece called "Imaginal Spreads and Pairs Trading" on exactly this topic, if you can find it (I couldn't find a copy on the public internet), originally published April 17, 2009. He writes: Academics and industry practitioners generally concentrate on time series aspects of currency ...


5

While triangular arbitrages exists, they are a rare, short lived, and shallow. In several academic datasets they are very rarely seen, mainly for two reasons, market efficiency aside: (1) the time resolution of the data is not tick by tick but aggregated at some level (for example at 1 second intervals), (2) the dataset doesn't include all available quotes ...


5

I am not sure why your question had so many upvotes because in currency markets anything else but triangular arbitrage does not exist. What is a quadrangular arb, I have never heard of it despite having traded fx among other asset classes for over ten years now. Think about it: Lets say you observe the price of EUR/USD. You can build triangular arbs by ...


5

Maybe not really an answer, but a justification of your approach. It's likely that your results can be expresses as $$ \mathsf EX_1 = 1.2\text{ and }\mathsf EX_2 = 2 $$ where $X_i$ for $i=1,2$ is a random pf of a situation in a class $i$ (we denote it $S_i$). Your method solves the following problem: given a fixed number of trials we would like to ...


5

It depends on what aspect of ZAR you are trying to take a position on. As A K pointed out, if your book is in USD and you want to take a position on the spot rate itself, then just have a USDZAR position. Yes, it is correlated with EURUSD because of both EUR-ZAR correlations and because of USD variations, but that's part of the USDZAR tradeoff. If, ...


5

You've got your calculation of the spread wrong, for what you're trying to do. Looking at the spot prices: SGD = USD 0.8, MXN = USD 0.077, NOK = USD 0.16. So in descending order they are SGD, NOK, MXN. The order of levels on your chart is SGD, NOK, MXN. INR vs CHF is the same: CHF = USD 1.1, INR = USD 0.017, so you get a larger spread for CHF in dollar ...


5

The CME' Fed Fund Futures are what you are looking for. http://www.cmegroup.com/trading/interest-rates/stir/30-day-federal-fund.html On settlement day they settle at the average overnight rate set by the Fed during the contract month.


5

The primary way ECNs determine if a liquidity taker's flow is 'toxic' or not is by looking at aftermath charts. The aftermath chart shows the average mark-to-market profit of trades done by the liquidity taker as a function of either time or number of top-of-book updates (optionally broken down by currency pair). The trade profit is usually viewed from the ...


5

I think you should look at it the other way around. Let $X_t$ denote the FOR/DOM spot exchange rate, i.e. 1 unit of foreign currency = $X_t$ units of domestic currency at time $t$. The FX forward rate $F^X(t,T)$ is defined as $$ F^X(t,T) = X_t \frac{B_f(t,T)}{B_d(t,T)} $$ by basence of arbitrage opportunity. To understand this, consider the following ...


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