Premium adjusted delta fx options

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Conversion of a premium-adjusted delta to a strike.
I am trying to compute the calibration of an FX market volatility surface, and especially I want to retrieve the strikes from the deltas quoted.
I don't have any trouble reverse-engineering the formulas for non premium-adjusted deltas. However, for many currency pairs, the convention is to use premium-adjusted deltas, which are not monotonic in strike. For example, for a premium-adjusted forward delta (Source: Clark - FX Option Pricing - Chap3 p47): $$ \Delta_ = \omega\frac >N(\omega d_ ) $$
One common solution to this problem is to search for strikes corresponding to deltas which are on the right hand side of the delta maximum.
What is the argument or the intuition behind this statement?

Premium adjusted delta fx options

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Strike / delta relationship for FX options.
I am tryinto find out how to go from delta to strike. If wee look at the bloomberg I am looking at 1M ATM volatility. I have included the Bloomberg data as a picture where we have following information: $f=0.9475$, $r=0.00274-0.02924$, $\sigma =13.32/100$, $T=1/12$, $t=0$.
The strike for $delta=0.488$ appears at the picture as well, and I try to recreate it. I use definition for the Black Sholes delta and I have this problem now:
$ SOLVE[e^ *N\left(d_1(k)\right)=0.4988]$ , $ k = 0.950417$
According to bloomberg this correct answer is $k=0.9483$. What went wrong? Personally I believe it's dates and time parameters that's not correct. According to Bjork: Arbitrage Theory in Continuous Time the time parameters need to measured in years. And in general. Is my approach correct?
I have found out about this method by looking at topics that are discussed here: Calculate strike from Black Scholes delta.
In FX world, the ATM strike is the delta-neutral strike, that is, the absolute delta values of a call and the corresponding put are the same. Moreover, the delta can be premium adjusted or not depending on the particular currency pair. See the linked paper as mentioned by AntoineConze.
For AUD/USD, the delta is not premium adjusted, and then the delta-neutral ATM strike is determined by the equation \begin \Phi(d_1) = \Phi(-d_1), \end that is, \begin K = Fe^ \sigma_ ^2 T>, \end where $F$ is the forward, $\sigma_ $ is the ATM volatility, and $T$ is the maturity. Based on the information you provided, \begin T&=\frac - \mbox > =0.090411,\\ K &= 0.9475\times e^ = 0.94826. \end See also Page 51 of the book Foreign Exchange Option Pricing by Iain J. Clark.
There are specific quotation conventions for specifying ATM and deltas for FX options quotes (unadjusted deltas, premium adjusted deltas, etc.) and converting deltas to strikes. These conventions vary across currency pairs.

Premium adjusted delta fx options

Value Vanilla FX Options Here.
The Vanilla FX Option Pricer allows its user to price a "Plain Vanilla" FX Option, i. e., either a European Call or a European Put .
The Strike (aka Exercise Price ) of the option may be specified either:
directly, as a Strike Value as a ratio of Strike to the Forward Rate as a Delta Target. In that latter case, the pricer will seek the Strike that corresponds to the specified Delta Target as the "At-The-Money" Strike: either the "At-The-Money-Forward" or the "Zero-Delta Straddle" Strike.
The input page layout is as follows:
Currency Pair : a drop-down list allowing the user to select the currency pair of the option.
Payoff Type : a drop-down list allowing the user to select either a Call or a Put option.
Maturity : a drop-down list allowing to user to select either:
a predetermined maturity, ranging from one week to one year.
a user-input actual exercise date.
Exercise Date : an input box for the user to input the date in the day, month, year format, only to be used if the selected maturity is "Actual Exercise Date"
Moneyness Type : a drop-down list allowing the user to select either:
Actual Strike , i. e., an actual value for the option's exercise price.
Ratio of the Strike to the Forward Rate , i. e., the ratio of the option' strike to the Forward FX Rate.
Left-Hand-Side Delta (protects option value in the underlying currency). The pricer will automatically adjust the Strike so that the option's Left-Hand-Side Delta be equal to the specified target.
Right-Hand-Side Delta (protects option value in the numéraire currency) . The pricer will automatically adjust the Strike so that the option's Right-Hand-Side Delta be equal to the specified target.
Exercise Price or Delta : an input box for the user to enter either the desired Strike or the Delta target, depending on the selected Moneyness Type. If no input is provided, then the pricer selects the At-The-Money Strike : either the Forward Rate (if Moneyness Type is not Delta) or the Zero-Delta Straddle Strike (if Moneyness Type is Delta)
Pricing is achieved by clicking on the “ Next ” button.
The pricing output is as follows.
Revalued at Market Close as of: Thu 13 Oct 2011.
USDJPY CALL.
Premium and Greeks.
The “ Premium and Greeks ” section gives the following information:
Value (or Premium ): this is the present value of the option, i. e., the premium that the dealer asks her client to pay to buy the option 1.
Delta : this is the sensitivity (first derivative) of the option's value (with respect) to the Spot FX Rate:
Left-Hand-Side Delta (LHS) denotes when the option's value is expressed in the underlying currency, for example the USD in a USDJPY Call 2.
Right-Hand-Side Delta (RHS) denotes when the option's value is expressed in the numéraire currency, for example the JPY in a USDJPY Call.
Gamma : this is the sensitivity of the Delta to the Spot FX Rate.
Vega : this is the sensitivity of the option's value to the Volatility of the FX Rate.
Theta : this is the sensitivity of the option's value to the passage of time, otherwise known as the Time Decay.
Vanna : this is the sensitivity of the vega to the Spot FX Rate.
Volga : this is the sensitivity of the Vega to the volatility of the FX Rate.
All results are given per unit of Notional Amount . The Notional Amount is the amount of the underlying asset concerned by the option, for example “a 1-year $1 million USD call at JPY 73.5”.
This is the option 3 to buy $1M worth of JPY at a price of JPY 73.5 per US Dollar, in one year.
The inventory of an options' trader is always denominated in terms of the Greeks . These quantities express the risk to which the trader's portfolio of options is exposed. For the Wikipedia explanation of Greeks, please Click Here.
For the Wikipedia explanation of Vanilla FX Options along with a Case Study, please Click Here.

How can I calculate the delta adjusted notional value?
Delta adjusted notional value is used to show the value of an option. This is different from most other derivatives, which use gross notional value or, in the case of interest rate derivatives, 10-year bond equivalent value. You can calculate the delta adjusted notional value of a portfolio by adding the options' weighted deltas together.
The delta adjusted notional value shows how valuable a replicated portfolio would be if it was comprised of a corresponding equity position only. For example, suppose a stock is trading at $70 and the delta of a call option is 0.8. This means that the value of the weighted delta for the option is $56 ($70 x 0.80).
Explaining Delta.
In derivatives trading terminology, "delta" refers to the sensitivity of the derivative price to changes in the price of the underlying asset.
An investor purchases 20 contracts of call options on a stock. If the stock goes up by 100% but the value of the contracts only increases by 75%, then the delta for the options is 0.75. Call option deltas are positive while put option deltas are negative.
Explaining Notional Value.
Notional value is the total market value of a leveraged position. This is easy to demonstrate with an indexed futures contract. One S&P 500 index future is worth 250 units of the S&P 500. Suppose the index is trading at $500; the notional value of the index is therefore $125,000 ($500 x 250).
Because options have a delta-dependent sensitivity, their notional value is not as straightforward as an indexed futures contract. Instead, the option's notional value needs to be adjusted based on the deltas inside the portfolio.
The easiest way to calculate this delta adjusted notional value is to calculate the delta for each individual option and add them together.