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Formula for forward price of bond

Amazingly, there are several different methods for computing bond forward price – the underlying ideas are the same (forward price = spot price - carry), but the computational details differ a bit ...
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13 votes
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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(...
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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 ...
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8 votes
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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 ...
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7 votes
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A proof that the final payoff on a futures contract is twice that on a forward contract

This part of your post In addition, on expiry day the holder (...) is wrong. [Short Story] Due to the daily variation margins calculated by the clearing house on each market close, you have ...
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6 votes
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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 ...
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6 votes
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FX Forward rate agreement valuation in quantlib

You are not giving the constructor a discountCurve. The constructor is: ...
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6 votes
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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 ...
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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 ...
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5 votes
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Prove arbitrage opportunity

Suppose that the given condition is true. You want to construct an arbitrage portfolio to take advantage of this. Now, $d$ is an interest rate, and the condition suggests that $d$ is too high. So you ...
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5 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: ...
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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}\...
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5 votes
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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. ...
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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) ...
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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 ...
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5 votes
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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-...
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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 ...
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4 votes
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BlackProcess' constructor $x_{0}$ argument in QuantLib

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 ...
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4 votes
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Forward rates formulae

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 ...
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4 votes

Calculate theoretical forward price of a stock

Let's use a no-arbitrage argument. Assume that the (continuously compounding) dividend yield is $q$ while the interest rate is $r$. For portfolio 1, we go long 1 forward contract with maturity $T$ ...
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4 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 ...
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4 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 ...
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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 ...
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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 ...
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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 ...
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4 votes
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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 ...
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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 ...
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4 votes
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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 ...
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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 ...
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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 \...
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