13
votes
Accepted
Convexity Adjustment for Futures
We assume that, under the probability measure $Q$,
\begin{align*}
dS_t &= S_t\big(r_t dt + \sigma dW_s(t)\big),\\
dr_t &= -k\, r_t dt + \alpha dW_r(t),\tag{1}
\end{align*}
where $d\langle W_s(...
- 21.3k
13
votes
Accepted
Why are FRA/futures convexity adjustments necessary?
This has been posted a few times now, so I will invest the time on a full response.
FRA / Futures convexity has nothing to do with profits/losses being immediately recognised on the future through ...
- 12.1k
11
votes
FX Option pricing on Forward vs. Spot
As long as you price on the outright forward and not on forward points (which is how most forwards are quoted in the market), this is essentially the same coin, looked at from different sides. If you ...
- 9,884
8
votes
When to Choose FX Swap or Forward
An FX swap exposes the user to a risk that is intrinsic to the interest rate differentials and supply and demand factors of one currency relative to another, but fundamentally there is negligible ...
- 12.1k
7
votes
Accepted
How to derive forward price on stock with continuous dividend
When the dividend yield $q$ is constant one can in fact derive a very simple forward formula under no model assumptions on $S_t$ (see (4) below). Only no arbitrage arguments are needed:
The forward ...
- 2,339
6
votes
FX forward curve building
I agree with dm63 in that cross-currency swap (CCS) is essential for building FX forward curve. Let me add/correct two things:
FX curve < 1 year can be backed out by FX forward contract. CCS is ...
- 1,214
6
votes
FX forward curve building
Your method assumes you can borrow or lend at OIS in both currencies, but in practice you cannot. That's why there is a current basis swap market , where you lend at OIS in one currency versus ...
- 17.9k
6
votes
Price a forward contract on a zero-coupon bond
Another way to obtain this result is, as I mentioned in the comment, to think about how you would replicate the forward contract. It has the following cash-flow structure:
...
- 6,094
6
votes
Accepted
Relationship between forward and option prices
At the heart of the (relative) pricing theory is the concept of no arbitrage and replication. I'll focus on equities here because as stated in the comments it may be more complicated for commodities.
...
- 14.8k
6
votes
Accepted
What is the instantaneous FX rate and used for a FX Forward?
If EURUSD Spot is currently trading at 1.21, then trading today for the usual settlement of EURUSD on today+2 would be at 1.21. If you wanted to trade for immediate exchange of EURUSD, what would be ...
- 3,719
6
votes
Accepted
Principal Components Analysis on overlapping contracts
I would do as follows:
A) First do PCA on an arbitrage-free monthly curve (assuming the most granular contract you will use is individual months). To ensure no arbitrages, you will need to drop out ...
- 1,671
6
votes
Accepted
FX Forward rate agreement valuation in quantlib
You are not giving the constructor a discountCurve. The constructor is:
...
- 5,895
6
votes
Accepted
what is the difference between an NDF and a FX Forward contract
Example of physical delivery FX forward:
In 1 month (maturity date or settlement date), I pay you USD 1 milion and receive from you EUR 1.2 million.
You can either specify both notionals in pay and ...
- 13.2k
6
votes
Accepted
How does a stock becoming hard to borrow affect puts and calls?
As you described, buying a put and selling a call in the hard to borrow stock, you have created a synthetic short future.
Like other equity finance positions, the "difficulty to borrow the stock&...
- 6,672
5
votes
Stochastic Interest rate spot forward relationship
The forward price $K$, determined at time $t$, is the amount such that the payoff at time $T$ is $S_T-K$, while the value at time $t$ is zero. That is,
\begin{align*}
B_t E\left(\frac{S_T-K}{B_T}\...
- 21.3k
5
votes
Mark to market forward contract
There are two types of contract (a) a forward contract and (b) a futures contract. In (a) there is no payment of margin on a daily basis. Its value is $(F_1-F_0)e^{-r(T-t)}$ as you describe. In (b) ...
- 17.9k
5
votes
Accepted
Pricing of forwards contracts
Decompose the first formula as $F_0=(S_0 - S_0(1-e^{-dT}))e^{rT}$ then let $PV_{I} = S_0(1-e^{-dT})$ which represents the present value of dividends (dividend rate = $d$) paid on the security during ...
- 5,702
5
votes
Accepted
Why has cross currency basis become higher since the 2008 crisis?
When you look at EUR/USD Cross Currency basis historical chart, you will notice that it was very similar in magnitude before 2008 to what it is now: in other words, there has always been some cross-...
- 6,490
5
votes
Curve Trades - Forward Swap vs Swap(Payer and Receiver)
Option 1 is not a steepener trade. It is an outright bearish trade that the 5y5y forward rate will move upwards. Option 2 is a steepener trade, if the dv01 is equal on the 5yr and 10yr legs. ...
- 17.9k
5
votes
Accepted
Trying to check this 1Y1Y forward treasuries calculation
I pulled up the Bloomberg page you referenced in your question. The rates you are referencing are not zero rates but yields on the coupon note/bond that are used to construct the curve. Toggle the ...
- 6,672
5
votes
Accepted
How to calculate FX Forward Rate to fit bloomberg
I'm just going to expand on AKdemy's comment. I don't have enough cred to comment (need 50).
As he said they'll never match due to being two fundamentally different sources. But assuming we do this ...
- 306
4
votes
Accepted
T-Forward measure
I think your statement has a typo. I can't find the statement you made in the article you cite.
The forward measure is the measure induced by using a bond as the numeraire instead of the risk free ...
- 1,439
4
votes
Some questions on (re-)pricing a forward
Assuming zero dividend and a constant interest rate $r$, the 1y forward price is then
\begin{align*}
120 = K = S_0 e^r = 100\, e^r.
\end{align*}
Consequently, $e^r = 1.2$. The fair value of the ...
- 21.3k
4
votes
Properly interpreting LIBOR curves?
Interest rate derivative trading relies on curves. The LIBOR rate, be it 1month, 3month, 6month etc is published and determined every day but derivative contracts continue to speculate on what futures ...
- 12.1k
4
votes
Constructing an FX forward curve
Interest rate parity is not sufficient now
There is a cross currency basis between the IRP result and observed market prices, because essentially Libor does not represent the cost of funding; in ...
- 3,719
4
votes
Accepted
Eurodollar future vs Eurodollar forward contracts
I guess the author's argument is that, because of the frequent settlements, one needs to invest the mark-to-market gains and fund the losses. As the exchange traded futures contract is negatively ...
- 5,173
4
votes
Why are some metals in contango (inverted) forward curve and some in backwardation (normal) forward curve?
There could be any number of explanations for copper to be backwardated and aluminum to be in contango right now.
The simplest (and most correct) explanation is the most vague: that these futures ...
- 2,972
4
votes
Accepted
forward contract on a defaultable zero-coupon bond
Based on notations in this question, assuming the market value recovery mechanism, the pre-default value at time $T_1$ of a zero-coupon bond with maturity $T_2$, where $T_1 < T_2$, is given by
\...
- 21.3k
4
votes
Accepted
How does this formula for the price of a bond in terms of forward rates work?
Assume today is $t$, and the 1st coupon pays at time $T_1$, the 2nd one at $T_2$, etc. Then your term structure of spot rates would be $R_1 = R(T_1) = f(t,T_1)$ for the 1st maturity, and $R_2 = R(T_2)$...
- 665
4
votes
Is the pricing formula for FX Forwards the same for FX Swaps?
Yes. The swap is quoted in fwd points relative to spot (sssuming that what you mean by r_term is the term interest rate of one currency and r_base the term interest rate of the other). Also, best to ...
- 6,672
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