Contract prices indicate a 79 percent probability that the currency will weaken this year and 33 percent odds that it will drop beyond 7 per dollar, a level last seen in 2008, according to Bloomberg calculations.

The article was published on 7 Jan 2016. How was the probabilities regarding Yuan's slump calculated from the options market?

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    $\begingroup$ In the BSM model N(d2) is the risk neutral probability that the option will end up in the money. I believe that s what they are talking about. So strictly speaking it is not a true probability. $\endgroup$
    – Alex C
    Jan 7, 2016 at 1:04
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    $\begingroup$ Could also be they used Litzenberer-Breeden formula. $\endgroup$
    – mbison
    Jan 7, 2016 at 23:36
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    $\begingroup$ I don't think N(d2) is the one they used. $\endgroup$
    – SmallChess
    Jan 8, 2016 at 0:41

2 Answers 2


Most traders have no idea what N(d2) is. I see two possibilities (a) they're using the delta of the option for the relevant strike, as seen by whatever model they're using, or (b) they are pricing a digital put on the yuan, using the full skew structure (as a former trader, that's the way I'd do it).

  • $\begingroup$ The Delta is N(d1), so how come they understand that and have no idea about N(d2) ;) $\endgroup$
    – nbbo2
    Jan 8, 2016 at 19:00
  • $\begingroup$ They don't know what N(d1) is either - they just know that the delta is approximately the probability of being in the money $\endgroup$
    – dm63
    Jan 9, 2016 at 21:27

there is nothing to do with implied distribution from option prices calculated with Breeden-Litzenberer approach. this distribution is "risk-neutral" not "real". consider this as a sort of theoretical and artificial, regarding to real disribution, idea. in the article the author wrote about demand for puts. so they/she calculated these probabilities from outstanding notional of different options with respect to each other. put/call ratio, open interest for given strike / total open interest etc. these "probabilities" are just a proxy. for example, you see OI for puts for strike=7 jumped significantly, does it mean that someone bets on exchange rate decline? well, no. there are several possible reasons for this to happen. for example someone hedges his position in calls, or someone buys risk reversals (buy call, sell put). so you buy puts, market makers sells them to you and delta-hedges at same moment... no bets on downside.


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