equivalent FX trades, succinctly

The equivalence among FX trades can be confusing to some. I feel there are only 2 common scenarios:

1) Buying usdjpy is equivalent to selling jpyusd.
2) Buying usdjpy call is equivalent to buying jpyusd put.

However, buying a fx option is never equivalent to selling an fx option. The seller wants (implied) vol to drop, whereas the buyer wants it to increase.


fxo premium as percentage of notional: mismatch

There’s an illustration in Tony’s lecture notes and also in the homework — 3 month 1.10 EUR call USD put, with Spot = 1.07
Assume the premium = 0.0200, given in USD per EUR
Then pnumccy = 0.0200, or a trader might say “200 USD pips”
”USD %” would be 0.0200/1.10 = 1.82%, pnumccy% = 0.0182
”EUR pips” would be 0.0182/1.07 = 0.0170 or “170 EUR pips”
”EUR %” would be 0.0200/1.07 = 1.87%, pbaseccy% = 0.0187

Observation — last line 1.87% means the premium is 1.87% of the EUR notional; the 1.82% means the same premium is 1.82% of the USD notional.

The paradox — the same premium is 1.87% of the EUR notional but only 1.82% of the USD notional !

(In general, paradoxes provide “aha” moments and great learning opportunity.)

Analysis (thin->thick->thin):

Key — the USD notional and EUR notional can have (vastly) different values before maturity.

Let’s focus on OTM (more common). Without loss of generality, let’s consider deep OTM. In such a case the EUR notional is almost worthless and the USD notional is a king’s ransom.

Naturally, the premium as percentage of the ransom is tiny.

fwd-starting fx swap points

Q: If 9M outright fwd point is 15.2 pips, and 3M is 5 pips, what would be the fwd-starting swap point?

A: The swap point would be 15.2 – 5 = 10.2 pips.

The fwd point for a 3Mo (our near date) is F – S = S (1 + R * 90/360)/(1 + r * 90/360) – S, which already considers the 3Mo length.

This formula shows the
* near date fwd point number is linear with (R – r).
* far date fwd point number is linear with (R – r).

However, the linear factors in these 2 cases are Different so it’s completely wrong to subtract like 12 – 5 basis points. Swap point reflects not only the IR differential, but also the “distance” and the spot level.

The swap points are smaller when the distance is short.

Suppose you as market take has an existing 3M fwd position and need to roll it forward. You effectively need to close the position for the original maturity and redo it at 9M. That’s 2 transactions with 2 dealers — unwise. Instead, You should go to one dealer to get a fwd-starting swap quote in bid/ask, without revealing your direction. The dealer would charge bid/ask only on the far leg, not twice on near leg and far leg.
Specifically, If there’s a bid/ask on the 3M fwd point (1.2 pip for eg), that doesn’t increase the swap point bid/ask spread, which would be the same bid/ask spread as the far leg fwd points.

-ve fwd points => ccy1 weakening => ccy1 higher inflation

(As we get older we rely increasingly on intuition)

Tony shared this quick intuition :
* when we see a …negative fwd point, we know ccy1 is …weakening due to … higher inflation in that country, such as AUD or BRL
* when we see a positive fwd point, we know ccy1 is strengthening due to ultra-low inflation such as EUR.

(Note the lowest inflation currency, JPY, is never a first currency…)

Remember ccy1ccy2 = 108.21 indicates the “strength of cc1”

– When we see ccy1 IR lower than ccy2, we know ccy1 will strengthen. You can imagine hyper-inflation in ccy2
– When we see ccy1 IR higher than ccy2, we know ccy1 will weaken. You can imagine hyper-inflation in ccy1

CIP ^ UIP, based on Mark Hendricks notes

Without loss of generality, Let’s suppose the loan period is “today + 12M”.

CIP (not UIP) is enforced by arbitrage and proven by real data. UIP is kind of naive theory, inconsistent with real data.

CIP relates 4 currently observed prices including a fwd exchange rate 12M forward (something like a rate lock). See http://bigblog.tanbin.com/2012/08/fx-fwd-arbitrage-4-ba-spreads-to.html

UIP relates 3 currently observed prices + a yet-unknown price —

E[spot rate 12M later] ) / spot rate = IntRate1/IntRrate2

Above expectation is in _physical_ measure i.e. wishful thinking (IMHO). CIP replaces that expectation with the risk-neutral E*[spot rate 12M later] := fwd contract price today.

RN basically means “backing out the forward contract’s valuation using live market data”. This back-out price is enforced by CIP arbitrage.

CIP arbitrage involves 4 trades done simultaneously. UIP can also involve several trades, but one of them is executed _12_M_ later, so the execution price is unknown now and could lose money.

compute FX swap bid/ask quotes from spotFX+IR quotes

Trac Consultancy’s coursebook has an example —

USD/IDR spot = 9150 / 9160
1m USD = 2.375% / 2.5%
1m IDR = 6.125% / 6.25%

Q: USD/IDR forward outright = ? / ?

Rule 1: treat first currency (i.e. USD) as a commodity like silver. Like all commodities, this one has a positive carry i.e. interest.

Rule 2: Immediately, notice our silver has lower interest than IDR, so silver is at fwd Premium, i.e. fwd price must be higher than spot.

Rule 3: in a simple zero-spread context, we know fwd price = spot * (1 + interest differential). This same formula still holds, but now we need to decide which spot bid/ask to use, which 1m-USD bid/ask to use, which 1m-IDR bid/ask to use.

Let’s say we want to compute the fwd _b_i_d_ price (rather than the ask) of the silver. The only fulfillment mechanism is — We the sell-side would borrow IDR, buy silver, lend the silver. At maturity, the total amount of silver divided by the amount of IDR would be same as my fwd bid price. In these 3 trades, we the sell-side would NOT cross the bid/ask spread even once, so we always use the favorable side of bid/ask, meaning

Use the Lower 1m-IDR
Use the Lower spot silver price
Use the Higher 1m-silver

Therefore fwd bid = 9150 [1 + (6.125%-2.5%)/12] = 9178

…… That’s the conclusion. Let’s reflect —

Rule 4: if we arrange the 4 numbers ascending – 2.375 / 2.5 / 6.125 / 6.25 then we always get interest differential between … either the middle pair (6.125-2.5) OR the outside pair (6.25-2.375). This is because the sell-side always uses the favorable quote of the lend and borrow.

Rule 5: We are working out the bid side, which is always lower than ask, so the spot quote to use has to be the bid. If the spot ask were used, it could be so much higher than the other side (for an illiquid pair) that the final fwd bid price is higher than the fwd ask! In fact this echos Rule 9 below.

Rule 5b: once we acquire the silver, we always lend it at the ask (i.e. 2.5). From Rule 4, the interest differential is (6.125-2.5)

Rule 9: As a dealer, always pick the favorable side when picking the spot, the IR on ccy1 and IR on ccy2.  If at any step you were to pick the unfavorable number, that number could be so extreme (huge bid/ask spread exists) as to make the final fwd bid Exceed the ask.

Let’s apply the rules on the fwd _a_s_k_ = 9160 [ 1+ (6.25% – 2.375%)/12 ] = 9190

Rule 1/2/3/4 same.

Apply Rule 5 – use spot ask (which is the higher quote). Once we sell silver spot, we lend the IDR sales proceeds at the higher side which is 6.25%….

most popular/important instruments by Singapore banks

I spoke to a derivative market data vendor’s presales. Let’s just say it’s a lady named AA.

Without referring specifically to Singapore market, she said in all banks (i guess she means trading departments) FX is the bread and butter. She said FX desk is the heaviest desk. She said interest rate might be the 2nd most important instrument. Equities and commodities are not …(heavy/active?) among banks.

I feel commercial banks generally like currencies and high quality bonds in favor of equities, unrated bonds and commodities. Worldwide, Commercial banks’ lending business model is most dependent on interest rates. Singapore being an import/export trading hub, its banks have more forex exposure than US or Japanese banks. Their use of credit products is interesting.

AA later cited credit derivative as potentially the 2nd most useful Derivative market data for a typical Singapore bank. (FXVol being the #1). Actually, Most banks don’t trade a lot of credit derivatives, but they need the market data for analysis (like CVA) and risk management. She gave an example — say your bank enters a long-term OTC contract with BNP. You need to assess BNP’s default probability as part of counterparty risk. The credit derivative market data would be relevant. I think the most common is CDS

(Remember this vendor is a specialist in derivative market data.)

The FX desk of most banks make bulk of the money from FXO, not FX spot. She felt spot volume is higher but margin is as low as 0.1 pip, with competition from EBS and other electronic liquidity venues. What she didn’t say is that FXO market is less crowded.

She agreed that many products are moving to the exchanges, but OTC model is more flexible.

RiskReversal -ve bid / +ve ask

Refer to the one-way RR quote in http://bigblog.tanbin.com/2012/06/fx-vol-quoting-convention.html.

Q1: What if 25Delta risk reversal bid/ask quotes are both positive?

As in the above example, dealer (say UBS) gives an RR Ask quote of 3.521%. Let’s say we have some hacker/insider friend to peek at UBS database, and we find the call’s Ask implied-vol is 9.521% and the put’s Bid implied-vol is 6%. In other words, dealer is willing to Write the 25Delta call at an annualized implied-vol of 9% and simultaneously Buy the Put @i-vol of 6%.

Now we ask the same dealer for a bid price. Dealer is bidding 2.8%. Our friend reveals that dealer is secretly willing to Buy the call @i-vol=8.9% (Lower quote) and simultaneously Write the put @i-vol=6.1% (Higher quote).

If you compare the bid vs ask on the call, as market maker the dealer is putting out 2-way quotes to buy low sell high.

If you compare the bid vs ask on the put, as market maker the dealer is putting out 2-way quotes to buy low sell high.

In this scenario, RR bid is below RR ask but both positive.

Q2: Could an RR bid be negative while the ask positive?

Ok We are serious about Selling an RR. To get a better bid price, we ask Dealer2 (SCB) for a Bid quote. Dealer is bidding -0.2%. Our insider tells us this dealer is willing to Buy the call @i-vol=5.9% and simultaneously Write the put @i-vol=6.1%

Between these dealers, Dealer1 would be the best (highest) bid. Now Dealer1 withdraws its quote. Dealer2 is the only bid. Market best RR bid is now negative.

Q2b: When would be RR bid and ask have opposite signs?
A: I guess when the 2 currencies are almost equal in terms of downside/upside

Q3: what if best RR bid and best RR ask are both negative? I think this is the norm in some currency pairs. Suppose market is bearish on the commodity currency (1st) and bullish on the quote currency (2nd). Treating commodity currency as an asset, Sink insurance costs more than surge insurance. Put premium exceeds Call premium. RR would be negative in both bid and ask.

risk reversal represents … skew sentiment

RR (risk reversal) is a quantitative indication of skew. As a key soft mkt datum, it focuses on and expresses a specific aspect of market sentiment. A lot of raw market data distill into this one number.

See P 118 [[FX analysis and trading]] (Bloomberg Press) — Positive RR represents bullish sentiment because call i-vol (surge-insurance premium) is higher than the comparable put i-vol (sink-insurance premium). That means more insurers feel surge is more likely than sink. Here we assume just 2 risks exist in this simplified world — surge and sink.

Another source says positive risk reversal implies a skewed distribution of expected spot returns composed of a relatively large number of small down moves and a relatively small number of large upmoves. But I find this statement ambiguous.

Note for equities, put i-vol always exceeds call i-vol, so skew is always negative. See other blogs.

In a wider context, there exists a wide range of transformations (and extractions) on raw data including historical, economic and issuer data. Techniques vary between markets. Even between 2 players on the same market the techniques can vary widely. There are entire professions dedicated to data analysis — quant strategists and quant analysts and quant traders. Among data transformations, RR is one of the most essential and part of the industry-standard.