Share-based payments (Tables)

12 Months Ended

Oct. 31, 2018

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Summary of Assumptions Used to Determine Fair Value of Options Granted

The following weighted-average assumptions were used as inputs into the Black-Scholes option pricing model to determine the fair value of options on the date of grant, excluding the options granted pursuant to the acquisition of The PrivateBank:

For the year ended October 31	2018			2017			2016
Weighted-average assumptions
Risk-free interest rate		2.08	%		1.58	%		1.34	%
Expected dividend yield		5.15	%		5.75	%		6.14	%
Expected share price volatility		14.74	%		14.53	%		17.26	%
Expected life		6 years			6 years			6 years
Share price/exercise price	$	120.02		$	110.83		$	97.73

Summary of Stock Option Activity and Related Information

Stock option plans

As at or for the year ended October 31				2018					2017					2016
	Number of stock options			Weighted- average exercise price  (1)		Number of stock options			Weighted- average exercise price		Number of stock options			Weighted- average exercise price
Outstanding at beginning of year		4,876,673		$	84.28		4,073,451		$	86.92		4,100,310		$	82.62
Granted		756,516			120.02		1,935,997			75.83		804,923			97.73
Exercised (2)		(876,309	)		67.84		(990,934	)		76.78		(815,767	)		75.86
Forfeited		(42,443	)		103.98		(133,581	)		99.77		(13,380	)		91.99
Cancelled/expired		(1,274	)		45.08		(8,260	)		58.99		(2,635	)		87.36
Outstanding at end of year		4,713,163		$	91.05		4,876,673		$	84.28		4,073,451		$	86.92
Exercisable at end of year		1,898,125		$	71.89		1,988,449		$	64.28		1,485,607		$	74.94
Available for grant		10,990,698					1,777,497					2,452,442

(1) For foreign currency-denominated options granted and exercised during the year, the weighted-average exercise prices are translated using exchange rates as at the grant date and settlement date, respectively. The weighted-average exercise price of outstanding balances as at October 31, 2018 reflects the conversion of foreign currency-denominated options at the year-end exchange rate.

(2) The weighted-average share price at the date of exercise was $120.55 (2017: $110.44; 2016: $99.66).

Summary of Stock Options Outstanding and Vested

Stock options outstanding and vested

As at October 31, 2018	Stock options outstanding						Stock options vested
Range of exercise prices	Number outstanding		Weighted- average contractual life remaining		Weighted- average exercise price		Number outstanding		Weighted- average exercise price
$11.00 – $55.00		406,223		3.53	$	30.99		406,223	$	30.99
$55.01 – $65.00		256,369		6.81		60.09		112,313		61.06
$65.01 – $75.00		309,799		2.41		71.21		308,942		71.22
$75.01 – $85.00		449,095		3.68		79.77		448,600		79.77
$85.01 – $95.00		401,117		5.28		90.92		383,443		90.86
$95.01 – $105.00		1,231,988		6.66		99.63		238,604		102.25
$105.01 – $115.00		1,658,572		8.59		114.95		–		–
		4,713,163		6.40	$	92.45		1,898,125	$	71.89