成交并非必然
朴素的回测假设任意大小的订单都按数据里的价格成交。真实订单要面对三个问题。订单簿有多深：市价单先吃最优报价，再吃下一档，所以大单的平均价格更差。市场是否触及我的限价：限价单能拿到你要的价格或更好，但前提是交易走到了那里。以及我能吃多少：大单只能占某根K线成交量的一小部分，所以要分批成交。
def fill_market_order(book, quantity):
remaining = quantity
cost = 0.0
filled = 0
for price, size in book: # cheapest offer first
if remaining <= 0:
break
take = min(size, remaining)
cost += take * price
filled += take
remaining -= take
if filled == 0:
return 0.0, 0
return cost / filled, filled
book = [(50.00, 300), (50.02, 500), (50.05, 1000)]
print(fill_market_order(book, 200)) # (50.0, 200) inside the first level
print(fill_market_order(book, 600)) # (50.01, 600) 300 at 50.00 and 300 at 50.02
print(fill_market_order(book, 5000)) # (50.0333, 1800) the whole book; 3,200 shares stay unfilled# The average price and the slippage against the best offer grow with the size
def average_price(book, quantity):
remaining, cost, filled = quantity, 0.0, 0
for price, size in book:
take = min(size, remaining)
cost += take * price
filled += take
remaining -= take
return cost / filled
book = [(50.00, 300), (50.02, 500), (50.05, 1000)]
for quantity in (100, 300, 800, 1800):
avg = average_price(book, quantity)
print(quantity, round(avg, 4), round((avg - 50.00) / 50.00 * 10000, 2), "bps above the best offer")限价单与跳空
用K线数据（开盘、最低、最高）看不到K线内部的路径，只能看到它的极值。在 L 的买入限价单，如果这根K线的最低价触及 L 或更低就成交。成交价是 L，除非这根K线开盘就低于 L：那是市场跳空越过了你的限价，你按开盘价成交，价格更好。卖出限价单是镜像。仅仅被触及的限价单在现实中可能不成交，因为排在你前面的队伍先被满足，所以这是乐观的上界。
def limit_fill(side, limit, bar_open, bar_low, bar_high):
if side == "buy" and bar_low <= limit:
return min(bar_open, limit) # a gap below the limit fills at the better open
if side == "sell" and bar_high >= limit:
return max(bar_open, limit)
return None
print(limit_fill("buy", 49.95, 50.10, 49.90, 50.20)) # 49.95 traded down through the limit
print(limit_fill("buy", 49.95, 49.90, 49.80, 50.20)) # 49.9 opened below: filled at the open
print(limit_fill("buy", 49.95, 50.10, 50.00, 50.20)) # None never reached
print(limit_fill("sell", 50.15, 50.00, 49.90, 50.20)) # 50.15处理大订单
许多执行台使用参与率上限：比如不超过成交量的 10%。在成交 40,000 股的K线里，上限是 4,000 股（向下取整）。于是一笔 5,000 股的订单要两根K线，而不是一根。逐根处理是一个携带剩余数量的循环：每根K线成交 min(remaining, int(volume * participation))，订单完成后的K线成交为零。
def partial_fill(quantity, bar_volume, participation):
return min(quantity, int(bar_volume * participation))
def fill_over_bars(quantity, volumes, participation):
remaining = quantity
fills = []
for volume in volumes:
filled = partial_fill(remaining, volume, participation)
fills.append(filled)
remaining -= filled
return fills
fills = fill_over_bars(5000, [40000, 30000, 80000, 100000], 0.1)
print(fills, sum(fills)) # [4000, 1000, 0, 0] 5000成交模型决定你的诚实程度这里每一处简化都偏向同一个方向：假设限价单一触及就成交、假设你从不推动市场、假设成交量总是够。结果越依赖成交假设，就越应该用悲观规则来检验（价格穿过限价才成交、降低参与率上限），看优势是否还在。
- 市价单逐档吃订单簿；平均价格按量加权，规模越大越差，订单簿薄时只能部分成交。
- 限价单在K线触及限价时成交，若跳空越过则按开盘价成交；仅仅触及在现实中可能不成交。
- 参与率上限把每根K线限制在
int(volume * participation)；循环把剩余数量带过各根K线。
下一节：CAPM 与贝塔，度量收益中有多少来自市场。
实验：评分内容
- 用
fill_market_order逐档吃单25 分 - 用
limit_fill判断限价是否成交25 分 - 用
partial_fill遵守成交量上限25 分 - 用
fill_over_bars分时间推进订单25 分