Variable Purchase Options [Loxx]Handley (2001) describes how to value variable purchase options (VPO). A VPO is basically a call option, but where the number of underlying shares is stochastic rather than fixed, or more precisely, a deterministic function of the asset price. The strike price of a VPO is typically a fixed discount to the underlying share price at maturity. The payoff at maturity is equal to max , where N is the number of shares. VPOs may be an interesting tool for firms that need to raise capital relatively far into the future at a given time. The number of underlying shares N is decided on at maturity and is equal to
N = X / St(1 -D)
where X is the strike price, ST is the asset price at maturity, and D is the fixed discount expressed as a proportion 0 > D < 1. The number of shares is in this way a deterministic function of the asset price. Further, the number of shares is often subjected to a minimum and maximum. In this case, we will limit the minimum number of shares to Nmin = X / U(1 -D) if, the asset price at maturity is above a predefined level U at maturity. Similarly, we will reach the maximum number of shares A T = x if the stock price at maturity is equal Nmax = X / L(1 -D) or lower than a predefined level L. Based on Handley (2001), we get the following closed-form solution: (via "The Complete Guide to Option Pricing Formulas")
c = XD / 1-D e^-rT + Nmin(Se^(b-r)T * N(d1) - Ue^-rT * N(d2))
- Nmax(Le^-rT * N(-d4) - Se^(b-r)T * N(-d3))
+ Nmax(L(1-D)e^-rT * N(-d6) - Se^(b-r)T * N(-d5))
where
d1 = (log(S/U) + (b+v^2/2)T) / vT^0.5 ... d2 = d1 - vT^0.5
d3 = (log(S/L) + (b+v^2/2)T) / vT^0.5 ... d4 = d3 - vT^0.5
d5 = (log(S/L(1-D)) + (b+v^2/2)T) / vT^0.5 ... d6 = d5 - vT^0.5
Inputs
Asset price (S)
Strike price (K)
Discount %
Lower bound
Upper bound
Time to maturity
Risk-free rate (r) %
Cost of carry (b) %
Volatility (v) %
Things to know
Only works on the daily timeframe and for the current source price.
You can adjust the text size to fit the screen
Exotic
NSDT Bearish-Bullish CandlesThis is another interesting take on candlesticks . These Bearish-Bullish Candles do not show the wicks. Instead, the upper wick is made into a Red body and the lower wick is made into a Green body. If you match the candle body color in the chart settings (or turn off the candles completely), you get a unique way of seeing how Bearish or how Bullish a candle is because the wick will now match the body size and color.
This indicator is very similar to our NSDT Special High-Low Candles.
Column XO ZoneColumn XO is an indicator in Prashant Shah's book Trading The Markets The Point & Figure Way. It counts a number of Xs and Os in every column for the length period. Both Xs and Os are calculated separately. Then, both results are divided by half the number of columns which is set by length.
I personally don't find this indicator very useful, because all it can offer is very clear in Point and Figure charts. However, it was designed to give some information on volatility as well as direction.
Good luck!
Column XOColumn XO is an indicator in Prashant Shah's book Trading The Markets The Point & Figure Way. It counts a number of Xs and Os in every column for the long period. Then, the result is divided by the number of columns which is set by length.
This indicator is designed to identify changes in volatility and works well with Wyckoff's Law of Cause and Effect. The longer the price spends in the consolidation, the more volatile and far-reaching should the expansion phase be.
Good luck!
NSDT Special High-Low CandlesThis is an interesting take on candlesticks. These special High-Low Candles do not show the Open and Close levels, so there are no wicks. However, you still see the the High and Low of the entire candle, giving you the full range.
Since this is an indicator, be sure to hide the chart candles to avoid overlap. Or choose offsetting colors to see the traditional candles under the indicator candles.
