Questions tagged [forward]

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9
votes
2answers
21k views

Formula for forward price of bond

What is the formula for the forward price of a bond (assuming there are coupons in the interim period, and that the deal is collateralised) Please also prove it with an arbitrage cashflow scenario ...
2
votes
2answers
2k views

Why are FRA/futures convexity adjustments necessary?

This would be my explanation for the reason that convexity adjustments must exist: Futures are margined daily, such that if a trader is paid a future and rates goes up then money is paid into their ...
11
votes
1answer
2k views

What do eigenvalues/eigenvectors of the yield/forward rates covariance matrices mean?

I have 5 bonds (with maturities 1,2,3,4,5 years) which I calculated the yield curve for 10 days. I also calculated the forward rates from the yield rates. Now I've been told to calculate the ...
5
votes
3answers
3k views

Price a forward contract on a zero-coupon bond

I'm trying to calculate the price of a forward contract on a zero-coupon bond (ZCB). The forward contract matures at $t_1$ and the ZCB matures at $t_2$. So is the price of the forwards contract just ...
6
votes
1answer
730 views

FX Forward pricing with correlation between FX and Zero-Cupon

I would like to extend my question about about FX Forward rates in stochastic interest rate setup: FX forward with stochastic interest rates pricing We consider a FX process $X_t = X_0 \exp( \int_0^t(...
2
votes
1answer
391 views

Characteristic functions for options on futures

Using simple delta-probability decomposition, the price European call options a non- dividend paying asset can be computed as \begin{equation} C(T,K) = {S_0}{\rm{ }}{\Pi _1} - {e^{ - rT}}K{\rm{ }}{\...
10
votes
1answer
6k views

Convexity Adjustment for Futures

Let $B_t$ be the cash account numeraire. The future and forward prices at time t are expressed as: $$ Fut = E_t^Q\left[S_T\right],$$ $$ Fwd = \frac{E_t^Q[S_T/B_T]}{E_t^Q[1/B_T]}.$$ Where $$ \frac{...
5
votes
3answers
5k views

Cross Currency Swap pricing

I have seen two methods for calculating the value of a xccy swap - 1) Convert the future foreign payments to the base currency using forward FX rates, net with the base currency payments and ...
16
votes
2answers
16k views

Why using 3 months forward to hedge fx risk on a fund of funds portfolio?

In my previous job, a fund of funds, they used 3 months forward FX contracts (renewed every 3 months) to protect their portfolio against currency risk. If I do understand why forwards are useful for ...
7
votes
2answers
1k views

VaR mapping - Forward Foreign Currency Contract

I have a question about VaR mapping for FX forwards. Please bear with me while I outline the problem. Philippe Jorion's book discusses VaR mapping; a means to break down complex instruments into ...
7
votes
1answer
26k views

Implied interest rate from FX swap

This is not homework. I am trying to calculate the implied interest rate of one currency (C2) using an FX swap and the interest rate of another currency (C1 - base). I have the following: Spot: 7....
0
votes
1answer
4k views

Why does increased stock borrow costs decrease a stock's forward price?

The author in this article -- http://streetwiseprofessor.com/?p=7294 -- states that an increase in stock borrowing costs decreases a stock's forward price: In the absence of manipulation, the ...
5
votes
2answers
7k views

How to derive Black's formula for the valuation of an option on a future?

I've got a question about 1976 Black Model and Bachelier model. I know that a geometric brownian motion in the P measure $dS_{t}=\mu S_{t}dt+\sigma S_{t} dW_{t}^{P}$ for a stock price $S_{t}$ leads (...
4
votes
0answers
2k views

Carry Trade vs synthetic Carry Trade using forward contracts

When it comes to foreign exchange carry trade strategy, the definition is straightforward: an investor borrows 1 US-\$ in the US (low interest country) and invests that \$1 to AU (high interest ...
1
vote
1answer
5k views

VaR for FX forwards

I am trying to figure out some of the commonly used approaches to deal with FX forwards (in a currency portfolio containing spots, forwards and swaps) that would allow me to calculate the one day VaR ...
2
votes
1answer
339 views

What is the filtration described?

What is the filtration $(\mathfrak{F}_t)$ encircled below? Is it $(\mathfrak{F}_t) = (\sigma(W_t)) = (\sigma(\tilde{W_t})), t \in [0,T]$? Or is it $(\mathfrak{F}_t) = (\sigma(\hat{W_t})), t \in [0,T]...
2
votes
3answers
310 views

How can I use the Radon-Nikodym theorem to show that forward measure is indeed measure?

The following statements are taken from the Wikipedia page for forward measure. Let $$B(T)=\exp \left(\int _{0}^{T}r(u)\,du\right)$$ be the bank account or money market account numeraire and $...
2
votes
2answers
205 views

Nature of short VIX strategies

By now, we all pretty much know that the recent upsurge in the VIX Index caused the spectacular failure of some Exchange-Traded Products (ETPs) or Exchange-Traded Notes (ETNs) written on it. An ...
1
vote
2answers
202 views

How does one calculate carry-roll-down theoretically assuming expectations of short-term rates are realised

I am not asking for an explanation that is hugely quantitative, but rather one that is more intuitive. I am aware that there are different assumptions that one could take when it comes to carry-roll-...
1
vote
2answers
916 views

Pricing Forward Start Option with PDE

I am looking for references (books and papers) or suggestions on how to price forward starting calls using a PDE approach typically in the Heston model (In the BS world, the computation is trivial), ...
0
votes
2answers
2k views

FX Option pricing on Forward vs. Spot

In a GBM world with riskless domestic and foreign interest rates, what would be the correct model for a FX plain vanilla option given the statement that this option is priced on the forward? I guess ...