Options & Strategies
Equity options are used to hedge equity positions against losses due to adverse changes in the equity market. Options are also used to for volatility views. Fees can be earned by selling options. Options are used in structured notes to enhance the yield in order to benefit from bullish/bearish equity market views.
In the pricers enter an equity code, strike and expiry date to load the current spot, smoothed implied volatility, rate and dividend yield. You may also enter values manually; the Surface and Rates and Inflation pages are available for reference.
Ensure you have read the User Agreement before using any calculators on RiskSnap.
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💲 Online Black-Scholes Option Pricer
Option Pricer 1
Option Pricer 2
About Options
• Equity Options
Equity options are priced using Black–Scholes.
Call: C = Se−qT N(d1) − Ke−rT N(d2)
Put: P = Ke−rT N(−d2) − Se−qT N(−d1)
d1 = ln(S/K) + (r − q + σ2/2)Tσ√T d2 = d1 − σ√T
S = spot; K = strike; T = time to expiry in years; r = interest rate; q = dividend yield; σ = volatility; N = standard normal cumulative distribution.
• Volatility
RiskSnap's volatility surface is used to determine market volatility. The volatility reflects current market prices for options with different strikes. This volatility is called “implied volatility (IV)” since it is implied from the option price which is a function of market demand. With the other components fixed at a point in time option price differences are due to differences in implied volatility. This is somewhat at odds of the statistical definition of volatility which is one standard deviation of historical returns about the mean regardless of strike. The differences create a surface which can be skewed to the left or right, or resemble a smile.
Market sources provide traded prices, bid/offer and IV for each listed option however illiquidity may make the IV out-of-date. This is sometimes accommodated by using recent bid/offer prices but the spreads may be wide for lack of depth. RiskSnap’s volatility surface uses Yahoo's closing prices to calculate RiskSnap IV and filters closing quotes that violate direction of puts and calls, removes some arbitrage impossibilities, applies monotonic filter checks since call prices should not rise as strike prices rise, or put prices should not fall as strikes rise and smoothes the result as a surface. At the extremes of the surface deep ITM/OTM options can be insensitive to volatility, making IV inferences difficult. Extrapolated parts of the surface deserve particular caution. The pricer uses Yahoo's forward annual dividend yield.
The “raw” surface on the Surface page displays Yahoo’s reported implied volatilities for reference. RiskSnap calculates its own implied volatilities from the option prices, then uses them to build the filtered smoothed surface used in its option pricing.
Strategies - Equity Options
Options are used both for hedging and for earning income. Strategies are combinations of options based on expectations of future movements of the underlying (spot), and volatilities. Risk, as for all capital markets instruments, always remains but the extent can be managed either through caps or through selling/buying back the option during the option’s life (to expiry).
Strategies can be used to build structured notes as in the costless collar.
In the following, for each of the strategies, the structure, the participant’s view and the maximum/minimum gains are listed. (fees which may or may not be required by the broker are not shown). Expiry dates are the same for all strategies and expressed in years, e.g. 30 days = .082192 years. ATM = At-the-money, OTM=out-of-the-money.
Please click on User Agreement before using any calculators on RiskSnap. User Agreement
Calculators for the above strategies follow. Each strategy uses percentage-based strikes and linked option panels. Each leg has its own volatility input and uses the RiskSnap pricing engine.
1. Bull Call Spread Calculator
Buy a lower strike call and sell a higher strike call. This is a debit spread.
Equity View: long | Volatility View: neutral
Bought Call
Sold Call
0% OTM means at the money; 5% OTM sets a call strike 5% above spot. Edit either the percentage or strike. Volatility, rate and dividend yield use decimals. The first Price button prices both legs.
Max loss: net premium paid. Max gain: higher strike less lower strike less net premium paid.
| Leg | Price per share | Delta per option | Cash Premium | Payoff at Spot |
|---|---|---|---|---|
| Bought Call | ||||
| Sold Call |
2. Bull Put Spread Calculator
Sell a higher strike put and buy a lower strike put. This is a credit spread.
Equity View: long | Volatility View: neutral
Buy Lower Put
Sell Higher Put
0% OTM means at the money. Positive % OTM sets call strikes above spot and put strikes below spot. Edit either the percentage or strike. Volatility, rate and dividend yield use decimals. The first Price button prices both legs.
Max loss: Higher strike less lower strike less net premium received. Max gain: Net premium received.
| Leg | Price per share | Delta per option | Cash Premium | Payoff at Spot |
|---|---|---|---|---|
| Buy Lower Put | ||||
| Sell Higher Put |
3. Bear Call Spread Calculator
Sell a lower strike call and buy a higher strike call. This is a credit spread.
Equity View: short | Volatility View: neutral
Sell Lower Call
Buy Higher Call
0% OTM means at the money. Positive % OTM sets call strikes above spot and put strikes below spot. Edit either the percentage or strike. Volatility, rate and dividend yield use decimals. The first Price button prices both legs.
Max loss: Higher strike less lower strike less net premium received. Max gain: Net premium received.
| Leg | Price per share | Delta per option | Cash Premium | Payoff at Spot |
|---|---|---|---|---|
| Sell Lower Call | ||||
| Buy Higher Call |
4. Bear Put Spread Calculator
Buy a higher strike put and sell a lower strike put. This is a debit spread.
Equity View: short | Volatility View: neutral
Sell Lower Put
Buy Higher Put
0% OTM means at the money. Positive % OTM sets call strikes above spot and put strikes below spot. Edit either the percentage or strike. Volatility, rate and dividend yield use decimals. The first Price button prices both legs.
Max loss: Net premium paid. Max gain: higher strike less lower strike less net premium paid.
| Leg | Price per share | Delta per option | Cash Premium | Payoff at Spot |
|---|---|---|---|---|
| Sell Lower Put | ||||
| Buy Higher Put |
5. Long Strangle Calculator
Buy an out-of-the-money put and an out-of-the-money call.
Equity View: neutral | Volatility View: Long
Buy OTM Put
Buy OTM Call
0% OTM means at the money. Positive % OTM sets call strikes above spot and put strikes below spot. Edit either the percentage or strike. Volatility, rate and dividend yield use decimals. The first Price button prices both legs.
Max loss: Net premium paid. Max gain: Unlimited.
| Leg | Price per share | Delta per option | Cash Premium | Payoff at Spot |
|---|---|---|---|---|
| Buy OTM Put | ||||
| Buy OTM Call |
6. Short Strangle Calculator
Sell an out-of-the-money put and an out-of-the-money call.
Equity View: neutral | Volatility View: Short
Sell OTM Put
Sell OTM Call
0% OTM means at the money. Positive % OTM sets call strikes above spot and put strikes below spot. Edit either the percentage or strike. Volatility, rate and dividend yield use decimals. The first Price button prices both legs.
Max loss: Unlimited. Max gain: Net premium received.
| Leg | Price per share | Delta per option | Cash Premium | Payoff at Spot |
|---|---|---|---|---|
| Sell OTM Put | ||||
| Sell OTM Call |
7. Long Straddle Calculator
Buy an at-the-money call and an at-the-money put.
Equity View: neutral | Volatility View: Long
Buy ATM Call
Buy ATM Put
0% OTM means at the money. Positive % OTM sets call strikes above spot and put strikes below spot. Edit either the percentage or strike. Volatility, rate and dividend yield use decimals. The first Price button prices both legs.
Max loss: Net premium paid. Max gain: Unlimited.
| Leg | Price per share | Delta per option | Cash Premium | Payoff at Spot |
|---|---|---|---|---|
| Buy ATM Call | ||||
| Buy ATM Put |
8. Short Straddle Calculator
Sell an at-the-money call and an at-the-money put.
Equity View: neutral | Volatility View: short
Sell ATM Call
Sell ATM Put
0% OTM means at the money. Positive % OTM sets call strikes above spot and put strikes below spot. Edit either the percentage or strike. Volatility, rate and dividend yield use decimals. The first Price button prices both legs.
Max loss: Unlimited. Max gain: Net premium received less difference between put strike and call strike if not exactly same. .
| Leg | Price per share | Delta per option | Cash Premium | Payoff at Spot |
|---|---|---|---|---|
| Sell ATM Call | ||||
| Sell ATM Put |
9. Negative Risk Reversal Calculator
Sell an out-of-the-money call and buy an out-of-the-money put.
Equity View: short | Volatility View: neutral
Buy OTM Put
Sell OTM Call
0% OTM means at the money. Positive % OTM sets call strikes above spot and put strikes below spot. Edit either the percentage or strike. Volatility, rate and dividend yield use decimals. The first Price button prices both legs.
Max loss: Unlimited. Max gain: Put strike less net premium paid.
| Leg | Price per share | Delta per option | Cash Premium | Payoff at Spot |
|---|---|---|---|---|
| Buy OTM Put | ||||
| Sell OTM Call |
10. Positive Risk Reversal Calculator
Buy an out-of-the-money call and sell an out-of-the-money put.
Equity View: long | Volatility View: neutral
Sell OTM Put
Buy OTM Call
0% OTM means at the money. Positive % OTM sets call strikes above spot and put strikes below spot. Edit either the percentage or strike. Volatility, rate and dividend yield use decimals. The first Price button prices both legs.
Max loss: Put strike less net premium received. Max gain: Unlimited.
| Leg | Price per share | Delta per option | Cash Premium | Payoff at Spot |
|---|---|---|---|---|
| Sell OTM Put | ||||
| Buy OTM Call |
11. Long Call Butterfly Spread Calculator
Buy one lower strike call, sell two middle calls, buy one higher strike call.
Equity View: neutral | Volatility View: Short
Buy Lower Call
Sell 2 Middle Calls
Buy Higher Call
0% OTM means at the money; negative % OTM means in the money. Positive % OTM sets calls above spot and puts below spot. Edit either the percentage or strike. Volatility, rate and dividend yield use decimals. The first Price button prices all legs.
Max loss: Net premium paid. Max gain: ATM strike less lower strike less net premium paid.
| Leg | Price per share | Delta per option | Cash Premium | Payoff at Spot |
|---|---|---|---|---|
| Buy Lower Call | ||||
| Sell 2 Middle Calls | ||||
| Buy Higher Call |
12. Short Call Butterfly Spread Calculator
Sell one lower strike call, buy two middle calls, sell one higher strike call.
Equity View: neutral | Volatility View: long
Sell Lower Call
Buy 2 Middle Calls
Sell Higher Call
0% OTM means at the money; negative % OTM means in the money. Positive % OTM sets calls above spot and puts below spot. Edit either the percentage or strike. Volatility, rate and dividend yield use decimals. The first Price button prices all legs.
Max loss: ATM strike less OTM strike less net premium received. Max gain: Net premium received.
| Leg | Price per share | Delta per option | Cash Premium | Payoff at Spot |
|---|---|---|---|---|
| Sell Lower Call | ||||
| Buy 2 Middle Calls | ||||
| Sell Higher Call |
13. Long Put Butterfly Spread Calculator
Buy one lower strike put, sell two middle puts, buy one higher strike put.
Equity View: neutral | Volatility View: short
Buy Lower Put
Sell 2 Middle Puts
Buy Higher Put
0% OTM means at the money; negative % OTM means in the money. Positive % OTM sets calls above spot and puts below spot. Edit either the percentage or strike. Volatility, rate and dividend yield use decimals. The first Price button prices all legs.
Max loss: Net premium paid. Max gain: ITM strike less 1 ATM strike less net premium paid.
| Leg | Price per share | Delta per option | Cash Premium | Payoff at Spot |
|---|---|---|---|---|
| Buy Lower Put | ||||
| Sell 2 Middle Puts | ||||
| Buy Higher Put |
14. Short Put Butterfly Spread Calculator
Sell one lower strike put, buy two middle puts, sell one higher strike put.
Equity View: neutral | Volatility View: long
Sell Lower Put
Buy 2 Middle Puts
Sell Higher Put
0% OTM means at the money; negative % OTM means in the money. Positive % OTM sets calls above spot and puts below spot. Edit either the percentage or strike. Volatility, rate and dividend yield use decimals. The first Price button prices all legs.
Max loss: 1 ATM strike less ITM strike less net premium received. Max gain: Net premium received.
| Leg | Price per share | Delta per option | Cash Premium | Payoff at Spot |
|---|---|---|---|---|
| Sell Lower Put | ||||
| Buy 2 Middle Puts | ||||
| Sell Higher Put |
15. Short Iron Condor Calculator
Buy a far OTM put, sell a nearer OTM put, sell a nearer OTM call, buy a farther OTM call.
Equity View: neutral | Volatility View: short
Buy Far OTM Put
Sell OTM Put
Sell OTM Call
Buy Far OTM Call
0% OTM means at the money; negative % OTM means in the money. Positive % OTM sets calls above spot and puts below spot. Edit either the percentage or strike. Volatility, rate and dividend yield use decimals. The first Price button prices all legs.
Max loss: Lower put strike less higher put strike, or, lower call strike less higher call strike; less net premium received . Max gain: Net premium received.
| Leg | Price per share | Delta per option | Cash Premium | Payoff at Spot |
|---|---|---|---|---|
| Buy Far OTM Put | ||||
| Sell OTM Put | ||||
| Sell OTM Call | ||||
| Buy Far OTM Call |
16. Long Iron Condor Calculator
Sell a far OTM put, buy a nearer OTM put, buy a nearer OTM call, sell a farther OTM call.
Equity View: neutral | Volatility View: long
Sell Far OTM Put
Buy OTM Put
Buy OTM Call
Sell Far OTM Call
0% OTM means at the money; negative % OTM means in the money. Positive % OTM sets calls above spot and puts below spot. Edit either the percentage or strike. Volatility, rate and dividend yield use decimals. The first Price button prices all legs.
Max loss: Net premium paid. Max gain: Higher put strike less lower put strike, or, higher call strike less lower call strike; less net premium paid.
| Leg | Price per share | Delta per option | Cash Premium | Payoff at Spot |
|---|---|---|---|---|
| Sell Far OTM Put | ||||
| Buy OTM Put | ||||
| Buy OTM Call | ||||
| Sell Far OTM Call |
17. Bullish Seagull Calculator
Buy a lower strike call, sell a higher strike call, and sell an OTM put.
Equity View: long | Volatility View: neutral
Sell OTM Put
Buy Lower Call
Sell Higher Call
. Uncheck to price all three entered strikes. The financing strike and % OTM update after pricing.
0% OTM means at the money; negative % OTM means in the money. Positive % OTM sets calls above spot and puts below spot. Edit either the percentage or strike. Volatility, rate and dividend yield use decimals. The first Price button prices all legs.
Max loss: Put strike . Max gain: Higher call strike less lower call strike.
| Leg | Price per share | Delta per option | Cash Premium | Payoff at Spot |
|---|---|---|---|---|
| Sell OTM Put | ||||
| Buy Lower Call | ||||
| Sell Higher Call |
18. Bearish Seagull Calculator
Sell a lower strike put, buy a higher strike put, and sell an OTM call.
Equity View: short | Volatility View: neutral
Sell Lower Put
Buy Higher Put
Sell OTM Call
. Uncheck to price all three entered strikes. The financing strike and % OTM update after pricing.
0% OTM means at the money; negative % OTM means in the money. Positive % OTM sets calls above spot and puts below spot. Edit either the percentage or strike. Volatility, rate and dividend yield use decimals. The first Price button prices all legs.
Max loss: Unlimited. Max gain: Higher put strike less lower put strike.
| Leg | Price per share | Delta per option | Cash Premium | Payoff at Spot |
|---|---|---|---|---|
| Sell Lower Put | ||||
| Buy Higher Put | ||||
| Sell OTM Call |